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Annotation 1729537903884

#geometry

An ellipsoid is a surface that may be obtained from a sphere by deforming it by means of directional scalings, or more generally, of an affine transformation.

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Ellipsoid - Wikipedia
= 1 : {\displaystyle {x^{2} \over a^{2}}+{y^{2} \over b^{2}}+{z^{2} \over c^{2}}=1:} sphere (top, a=b=c=4), spheroid (bottom left, a=b=5, c=3), tri-axial ellipsoid (bottom right, a=4.5, b=6, c=3) An ellipsoid is a surface that may be obtained from a sphere by deforming it by means of directional scalings, or more generally, of an affine transformation. An ellipsoid is a quadric surface, that is a surface that may be defined as the zero set of a polynomial of degree two in three variables. Among quadric surfaces, an ellipsoid is char

Annotation 1729593478412

#finance

In finance, mean reversion is the assumption that a stock's price will tend to move to the average price over time.

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Mean reversion (finance) - Wikipedia
ocultar ahora Mean reversion (finance) From Wikipedia, the free encyclopedia Jump to: navigation, search For other uses, see Mean reversion (disambiguation). In finance, mean reversion is the assumption that a stock's price will tend to move to the average price over time. [1] [2] Using mean reversion in stock price analysis involves both identifying the trading range for a stock and computing the average price using analytical techniques taking into ac

Flashcard 1729595837708

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#finance

Question

In finance, [...] is the assumption that a stock's price will tend to move to the average price over time.

Answer

mean reversion

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In finance, mean reversion is the assumption that a stock's price will tend to move to the average price over time.

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Flashcard 1729615760652

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#gaussian-process

Question

isotropic process depend only on distance, not [...]

Answer

direction

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If the process depends only on |x − x'|, the Euclidean distance (not the direction) between x and x', then the process is considered isotropic.

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Gaussian process - Wikipedia
stationary, it depends on their separation, x − x', while if non-stationary it depends on the actual position of the points x and x'. For example, the special case of an Ornstein–Uhlenbeck process, a Brownian motion process, is stationary. If the process depends only on |x − x'|, the Euclidean distance (not the direction) between x and x', then the process is considered isotropic. A process that is concurrently stationary and isotropic is considered to be homogeneous; [7] in practice these properties reflect the differences (or rather the lack of them) in the behaviour of the process given the location of the observer. Ultimately Gaussian processes translate as taking priors on functions and the smoothness of these priors can be induced by the covariance function. [5] If we expect that for "ne

Flashcard 1729661111564

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#geometry

Question

An [...] may be obtained by deforming a sphere with an affine transformation .

Answer

ellipsoid

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An ellipsoid is a surface that may be obtained from a sphere by deforming it by means of directional scalings, or more generally, of an affine transformation.

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Flashcard 1729662684428

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#geometry

Question

An ellipsoid may be obtained by deforming a sphere with an [...].

Answer

affine transformation

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An ellipsoid is a surface that may be obtained from a sphere by deforming it by means of directional scalings, or more generally, of an affine transformation.

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Annotation 1729724550412

#quantecon

OOP is about producing well organized code — an important determinant of productivity

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Object Oriented Programming – Quantitative Economics
ramming, and nicely supported in Python OOP has become an important concept in modern software engineering because It can help facilitate clean, efficient code (if used well) The OOP design pattern fits well with many computing problems OOP is about producing well organized code — an important determinant of productivity Moreover, OOP is a part of Python, and to progress further it’s necessary to understand the basics About OOP¶ OOP is supported in many languages: JAVA and Ruby are relativel

Flashcard 1731011939596

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#quantecon

Question

OOP is about producing [...] — an important determinant of productivity

Answer

well organized code

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OOP is about producing well organized code — an important determinant of productivity

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Annotation 1731471478028

#reinforcement-learning

Mountain Car, a standard testing domain in Reinforcement Learning, is a problem in which an under-powered car must drive up a steep hill. Since gravity is stronger than the car's engine, even at full throttle, the car cannot simply accelerate up the steep slope. The car is situated in a valley and must learn to leverage potential energy by driving up the opposite hill before the car is able to make it to the goal at the top of the rightmost hill. The domain has been used as a test bed in various Reinforcement Learning papers.

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Mountain car problem - Wikipedia
[imagelink] This article is an orphan, as no other articles link to it. Please introduce links to this page from related articles; try the Find link tool for suggestions. (July 2012) [imagelink] The mountain car problem Mountain Car, a standard testing domain in Reinforcement Learning, is a problem in which an under-powered car must drive up a steep hill. Since gravity is stronger than the car's engine, even at full throttle, the car cannot simply accelerate up the steep slope. The car is situated in a valley and must learn to leverage potential energy by driving up the opposite hill before the car is able to make it to the goal at the top of the rightmost hill. The domain has been used as a test bed in various Reinforcement Learning papers. Contents [hide] 1 Introduction 2 History 3 Techniques used to solve mountain car 3.1 Discretization 3.2 Function approximation 3.3 Traces 4 Technical details 4.1 State v

Annotation 1731505294604

#reinforcement-learning

Mountain Car, a standard testing domain in Reinforcement Learning, is a problem in which an under-powered car must drive up a steep hill.

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Mountain Car, a standard testing domain in Reinforcement Learning, is a problem in which an under-powered car must drive up a steep hill. Since gravity is stronger than the car's engine, even at full throttle, the car cannot simply accelerate up the steep slope. The car is situated in a valley and must learn to leverage p

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Flashcard 1731506867468

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#reinforcement-learning

Question

Mountain Car, a standard testing domain in Reinforcement Learning, is a problem in which an [...] must drive up a steep hill.

Answer

under-powered car

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Mountain Car, a standard testing domain in Reinforcement Learning, is a problem in which an under-powered car must drive up a steep hill.

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Annotation 1731635318028

#linear-algebra

In mathematics, a linear map (also called a linear mapping, linear transformation or, in some contexts, linear function) is a mapping V → W between two modules (including vector spaces) that preserves (in the sense defined below) the operations of addition and scalar multiplication.

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Linear map - Wikipedia
Linear operator) Jump to: navigation, search "Linear transformation" redirects here. For fractional linear transformations, see Möbius transformation. Not to be confused with linear function. In mathematics, a linear map (also called a linear mapping, linear transformation or, in some contexts, linear function) is a mapping V → W between two modules (including vector spaces) that preserves (in the sense defined below) the operations of addition and scalar multiplication. An important special case is when V = W, in which case the map is called a linear operator, [1] or an endomorphism of V. Sometimes the term linear function has the same meaning as li

Flashcard 1731637415180

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#linear-algebra

Question

An important special case (of linear mapping) is when V = W , in which case the map is called a [...] ,^[1] or an endomorphism of V .

Answer

linear operator

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Linear map - Wikipedia
linear mapping, linear transformation or, in some contexts, linear function) is a mapping V → W between two modules (including vector spaces) that preserves (in the sense defined below) the operations of addition and scalar multiplication. An important special case is when V = W, in which case the map is called a linear operator, [1] or an endomorphism of V. Sometimes the term linear function has the same meaning as linear map, while in analytic geometry it does not. A linear map always maps linear subspaces onto linear subspaces (possibl

Flashcard 1731639774476

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#linear-algebra

Question

a linear map is a mapping V → W that preserves the operations of [...].

Answer

addition and scalar multiplication

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thematics, a linear map (also called a linear mapping, linear transformation or, in some contexts, linear function) is a mapping V → W between two modules (including vector spaces) that preserves (in the sense defined below) the operations of addition and scalar multiplication. <body><html>

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Annotation 1731642658060

#matrices #spectral-theorem

In mathematics, particularly linear algebra and functional analysis, a spectral theorem is a result about when a linear operator or matrix can be diagonalized (that is, represented as a diagonal matrix in some basis).

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Spectral theorem - Wikipedia
for more information. [imagelink] [Help with translations!] Spectral theorem From Wikipedia, the free encyclopedia Jump to: navigation, search In mathematics, particularly linear algebra and functional analysis, a spectral theorem is a result about when a linear operator or matrix can be diagonalized (that is, represented as a diagonal matrix in some basis). This is extremely useful because computations involving a diagonalizable matrix can often be reduced to much simpler computations involving the corresponding diagonal matrix. The concep

Flashcard 1731644755212

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#matrices #spectral-theorem

Question

[...] is a result about when a linear operator or matrix can be diagonalized

Answer

spectral theorem

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In mathematics, particularly linear algebra and functional analysis, a spectral theorem is a result about when a linear operator or matrix can be diagonalized (that is, represented as a diagonal matrix in some basis).

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Flashcard 1731703737612

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#finance

Question

The Black–Scholes model is a mathematical model of a financial market containing [...] instruments

Answer

derivative investment

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The Black–Scholes / ˌ b l æ k ˈ ʃ oʊ l z / [1] or Black–Scholes–Merton model is a mathematical model of a financial market containing derivative investment instruments. From the partial differential equation in the model, known as the Black–Scholes equation, one can deduce the Black–Scholes formula, which gives a theoretical estimate of the price of E

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Black–Scholes model - Wikipedia
Black–Scholes model - Wikipedia Black–Scholes model From Wikipedia, the free encyclopedia (Redirected from Black–Scholes) Jump to: navigation, search The Black–Scholes /ˌblæk ˈʃoʊlz/ [1] or Black–Scholes–Merton model is a mathematical model of a financial market containing derivative investment instruments. From the partial differential equation in the model, known as the Black–Scholes equation, one can deduce the Black–Scholes formula, which gives a theoretical estimate of the price of European-style options and shows that the option has a unique price regardless of the risk of the security and its expected return (instead replacing the security's expected return with the risk-neutral rate). The formula led to a boom in options trading and provided mathematical legitimacy to the activities of the Chicago Board Options Exchange and other options markets around the world. [2]

Flashcard 1731730476300

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#stochastics

Question

The Wiener process starts at [...

Answer

a.s.

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The Wiener process is characterised by the following properties: [1] a.s. has independent increments: for every the future increments , are independent of the past values , has Gaussian increments: is normally distributed with mean and variance ,

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Wiener process - Wikipedia
Brownian motion 4.3 Time change 4.4 Change of measure 4.5 Complex-valued Wiener process 4.5.1 Self-similarity 4.5.2 Time change 5 See also 6 Notes 7 References 8 External links Characterisations of the Wiener process[edit source] The Wiener process W t {\displaystyle W_{t}} is characterised by the following properties: [1] W 0 = 0 {\displaystyle W_{0}=0} a.s. W {\displaystyle W} has independent increments: for every t > 0 , {\displaystyle t>0,} the future increments W t + u − W t , {\displaystyle W_{t+u}-W_{t},} u ≥ 0 , {\displaystyle u\geq 0,} , are independent of the past values W s {\displaystyle W_{s}} , s ≤ t . {\displaystyle s\leq t.} W {\displaystyle W} has Gaussian increments: W t + u − W t {\displaystyle W_{t+u}-W_{t}} is normally distributed with mean 0 {\displaystyle 0} and variance u {\displaystyle u} , W t + u − W t ∼ N ( 0 , u ) . {\displaystyle W_{t+u}-W_{t}\sim {\mathcal {N}}(0,u).} W {\displaystyle W} has continuous paths: With probability 1 {\displaystyle 1} , W t {\displaystyle W_{t}} is continuous in t {\displaystyle t} . The independent increments means that if 0 ≤ s 1 < t 1 ≤ s 2 < t 2 then W t 1 −W s 1 and W t 2 −W s 2 are independent random variables, and the similar condition holds for

Flashcard 1732507733260

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#spanish

Question

▸ ¡ [...] una respuesta!
I demand an answer!

Answer

exijo

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Annotation 1732660825356

#matrices #spectral-theorem

In general, the spectral theorem identifies a class of linear operators that can be modeled by multiplication operators, , which are as simple as one can hope to find.

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Spectral theorem - Wikipedia
putations involving the corresponding diagonal matrix. The concept of diagonalization is relatively straightforward for operators on finite-dimensional vector spaces but requires some modification for operators on infinite-dimensional spaces. In general, the spectral theorem identifies a class of linear operators that can be modeled by multiplication operators, which are as simple as one can hope to find. In more abstract language, the spectral theorem is a statement about commutative C*-algebras. See also spectral theory for a historical per

Flashcard 1732662398220

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#matrices #spectral-theorem

Question

In general, the spectral theorem identifies a class of [...] that can be modeled by multiplication operators

Answer

linear operators

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In general, the spectral theorem identifies a class of linear operators that can be modeled by multiplication operators

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Flashcard 1732663971084

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#matrices #spectral-theorem

Question

In general, the spectral theorem identifies a class of linear operators that can be modeled by [...]

Answer

multiplication operators

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In general, the spectral theorem identifies a class of linear operators that can be modeled by multiplication operators

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Annotation 1732735536396

#linear-algebra

In mathematics, more specifically in abstract algebra and linear algebra, a bilinear form on a vector space V is a bilinear map V × V → K , where K is the field of scalars. In other words, a bilinear form is a function B : V × V → K that is linear in each argument separately:

B(u + v, w) = B(u, w) + B(v, w) and B(λu, v) = λB(u, v)
B(u, v + w) = B(u, v) + B(u, w) and B(u, λv) = λB(u, v)

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Bilinear form - Wikipedia
Bilinear form - Wikipedia Bilinear form From Wikipedia, the free encyclopedia Jump to: navigation, search In mathematics, more specifically in abstract algebra and linear algebra, a bilinear form on a vector space V is a bilinear map V × V → K, where K is the field of scalars. In other words, a bilinear form is a function B : V × V → K that is linear in each argument separately: B(u + v, w) = B(u, w) + B(v, w) and B(λu, v) = λB(u, v) B(u, v + w) = B(u, v) + B(u, w) and B(u, λv) = λB(u, v) The definition of a bilinear form can be extended to include modules over a ring, with linear maps replaced by module homomorphisms. When K is the field of complex numbers C, one

Flashcard 1732737633548

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#linear-algebra

Question

a bilinear form is [...descriptive]

Answer

linear in each argument separately

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In mathematics, more specifically in abstract algebra and linear algebra, a bilinear form on a vector space V is a bilinear map V × V → K , where K is the field of scalars. In other words, a bilinear form is a function B : V × V → K that is linear in each argument separately: B(u + v, w) = B(u, w) + B(v, w) and B(λu, v) = λB(u, v) B(u, v + w) = B(u, v) + B(u, w) and B(u, λv) = λB(u, v) <body><html>

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Flashcard 1736018889996

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#stochastics

Question

a homogeneous Poisson process is defined with a [...]

Answer

single positive constant

The constant denotes a fixed area (or length) on the domain.

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If a Poisson process is defined with a single positive constant, then the process is called a homogeneous Poisson process.

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Stochastic process - Wikipedia
arameter. This process has the natural numbers as its state space and the non-negative numbers as its index set. This process is also called the Poisson counting process, since it can be interpreted as an example of a counting process. [99] If a Poisson process is defined with a single positive constant, then the process is called a homogeneous Poisson process. [99] [101] The homogeneous Poisson process (in continuous time) is a member of important classes of stochastic processes such as Markov processes and Lévy processes. [49] The homogen

Flashcard 1736250101004

Tags

#poisson-process #stochastics

Question

if [...] in some space forms a Poisson process, then the number of points in a region of finite size is a random variable with a Poisson distribution.

Answer

a collection of random points

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Its name (Poisson Process) derives from the fact that if a collection of random points in some space forms a Poisson process, then the number of points in a region of finite size is a random variable with a Poisson distribution.

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Poisson point process - Wikipedia
oint processes, some of which are constructed with the Poisson point process, that seek to capture such interaction. [22] The process is named after French mathematician Siméon Denis Poisson despite Poisson never having studied the process. Its name derives from the fact that if a collection of random points in some space forms a Poisson process, then the number of points in a region of finite size is a random variable with a Poisson distribution. The process was discovered independently and repeatedly in several settings, including experiments on radioactive decay, telephone call arrivals and insurance mathematics. [23] [24] T

Flashcard 1737336950028

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#lists #python

Question

An map operation “maps” a function onto [...] in a sequence.

Answer

each of the elements

like capitalize_all

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An operation like capitalize_all is sometimes called a map because it “maps” a function (in this case the method capitalize ) onto each of the elements in a sequence.

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Lists
ngs: def capitalize_all(t): res = [] for s in t: res.append(s.capitalize()) return res res is initialized with an empty list; each time through the loop, we append the next element. So res is another kind of accumulator. An operation like capitalize_all is sometimes called a map because it “maps” a function (in this case the method capitalize) onto each of the elements in a sequence. Another common operation is to select some of the elements from a list and return a sublist. For example, the following function takes a list of strings and returns a list that cont

Annotation 1737342979340

#numpy

Fancy indexing is conceptually simple: it means passing an array of indices to access multiple array elements at once.

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Fancy Indexing | Python Data Science Handbook
is like the simple indexing we've already seen, but we pass arrays of indices in place of single scalars. This allows us to very quickly access and modify complicated subsets of an array's values. Exploring Fancy Indexing¶ Fancy indexing is conceptually simple: it means passing an array of indices to access multiple array elements at once. For example, consider the following array: In [1]: import numpy as np rand = np.random.RandomState(42) x = rand.randint(100, size=10) print(x)

Flashcard 1737345076492

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#numpy

Question

[...] is conceptually simple: it means passing an array of indices to access multiple array elements at once.

Answer

Fancy indexing

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Fancy indexing is conceptually simple: it means passing an array of indices to access multiple array elements at once.

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Flashcard 1737346649356

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#numpy

Question

Fancy indexing passes [...] to access multiple array elements at once.

Answer

an array of indices

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Fancy indexing is conceptually simple: it means passing an array of indices to access multiple array elements at once.

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Flashcard 1737348222220

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#numpy

Question

Fancy indexing is conceptually simple: it means passing an array of indices to access [...] at once.

Answer

multiple array elements

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Fancy indexing is conceptually simple: it means passing an array of indices to access multiple array elements at once.

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Annotation 1737942502668

#numpy

It is always important to remember with fancy indexing that the return value reflects the broadcasted shape of the indices, rather than the shape of the array being indexed

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Fancy Indexing | Python Data Science Handbook
exactly as we saw in broadcasting of arithmetic operations. For example: In [8]: row[:, np.newaxis] * col Out[8]: array([[0, 0, 0], [2, 1, 3], [4, 2, 6]]) It is always important to remember with fancy indexing that the return value reflects the broadcasted shape of the indices, rather than the shape of the array being indexed. Combined Indexing¶ For even more powerful operations, fancy indexing can be combined with the other indexing schemes we've seen: In [9]: print

Flashcard 1737944075532

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#numpy

Question

It is always important to remember with fancy indexing that the return value reflects [...], rather than the shape of the array being indexed

Answer

the broadcasted shape of the indices

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It is always important to remember with fancy indexing that the return value reflects the broadcasted shape of the indices, rather than the shape of the array being indexed

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Annotation 1738454207756

#spanish

El entrenador portugués desestimó los argumentos del City y Guardiola por los que desistieron de contratar al jugador chileno.

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Noticias, Estadísticas y Resultados de Premiership de Inglaterra - ESPNDEPORTES - ESPNDeportes
icas Estadísticas [imagelink] [imagelink] Manchester United/Man Utd via Getty Images 2hRob Dawson, ESPN Mourinho: Alexis no se mudó al United por dinero El entrenador portugués desestimó los argumentos del City y Guardiola por los que desistieron de contratar al jugador chileno. [imagelink]play Guido Carrillo, nuevo jugador de Southampton (0:24) [imagelink]play0:24 9h Carrillo pasó al Southampton de Pellegrino El mediocampista ex-Estudiantes ya fue oficializado

Flashcard 1738481208588

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#spanish

Question

El [...] portugués desestimó los argumentos del City y Guardiola por los que desistieron de contratar al jugador chileno.

Answer

entrenador

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El entrenador portugués desestimó los argumentos del City y Guardiola por los que desistieron de contratar al jugador chileno.

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Annotation 1738484092172

#spanish

El entrenador del Chelsea destacó que, considerando la inversiones del City y United, el título de liga de la temporada pasada fue un "pequeño milagro".

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Noticias, Estadísticas y Resultados de Premiership de Inglaterra - ESPNDEPORTES - ESPNDeportes
Arsenal La leyenda gunner salió al cruce de los rumores que afirmaban que había influido en el pase del chileno al United. [imagelink] Darren Walsh/Chelsea FC via Getty Images 2dLiam Twomey, ESPN Conte: Chelsea no puede gastar como Manchester El entrenador del Chelsea destacó que, considerando la inversiones del City y United, el título de liga de la temporada pasada fue un "pequeño milagro". [imagelink]play João Castelo-Branco traz todas as novidades da movimentação do mercado na Inglaterra (6:34) [imagelink]play Liverpool se estrelló ante Swansea City (1:25) [imagelink]pla

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#spanish

Question

El entrenador del Chelsea destacó que, considerando las [...] del City y United, el título de liga de la temporada pasada fue un "pequeño milagro".

Answer

inversiones

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El entrenador del Chelsea destacó que, considerando la inversiones del City y United, el título de liga de la temporada pasada fue un "pequeño milagro".

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#spanish

Question

El entrenador del Chelsea destacó que, considerando la inversiones del City y United, el título de liga de la temporada pasada fue un "pequeño [...]".

Answer

milagro

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El entrenador del Chelsea destacó que, considerando la inversiones del City y United, el título de liga de la temporada pasada fue un "pequeño milagro".

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#measure-theory

The Cantor ternary set is created by iteratively deleting the open middle third from a set of line segments.

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Cantor set - Wikipedia
bability 3.7 Cantor numbers 4 Variants 4.1 Smith–Volterra–Cantor set 4.2 Stochastic Cantor set 4.3 Cantor dust 5 Historical remarks 6 See also 7 Notes 8 References 9 External links Construction and formula of the ternary set[edit] The Cantor ternary set C {\displaystyle {\mathcal {C}}} is created by iteratively deleting the open middle third from a set of line segments. One starts by deleting the open middle third (1/3, 2/3) from the interval [0, 1], leaving two line segments: [0, 1/3] ∪ [2/3, 1]. Next, the open middle third of each of these remaining

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#measure-theory #stochastics

Question

[...] gives the same result as Riemann integration when the latter exists

Answer

Lebesgue integration

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Lebesgue integration or abstract integration gives the same result as Riemann integration when the latter exists, so nothing you know from calculus changes, but a lot more functions are integrable <

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#measure-theory

Question

The [...] is created by iteratively deleting the open middle third from a set of line segments.

Answer

Cantor ternary set

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The Cantor ternary set is created by iteratively deleting the open middle third from a set of line segments.

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#measure-theory

Question

The Cantor ternary set is created by iteratively deleting [...] from a set of line segments.

Answer

the open middle third

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The Cantor ternary set is created by iteratively deleting the open middle third from a set of line segments.

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#bayesian-network

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In Bayesian networks each node represents a variable with [...]

Answer

a probability distribution

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ayesian network) represent variables that are conditionally independent of each other. Each node is associated with a probability function that takes, as input, a particular set of values for the node's parent variables, and gives (as output) the probability (or probability distribution, if applicable) of the variable represented by the node. <body><html>

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Bayesian network - Wikipedia
ed acyclic graph (DAG). For example, a Bayesian network could represent the probabilistic relationships between diseases and symptoms. Given symptoms, the network can be used to compute the probabilities of the presence of various diseases. Formally, Bayesian networks are DAGs whose nodes represent variables in the Bayesian sense: they may be observable quantities, latent variables, unknown parameters or hypotheses. Edges represent conditional dependencies; nodes that are not connected (there is no path from one of the variables to the other in the Bayesian network) represent variables that are conditionally independent of each other. Each node is associated with a probability function that takes, as input, a particular set of values for the node's parent variables, and gives (as output) the probability (or probability distribution, if applicable) of the variable represented by the node. For example, if m {\displaystyle m} parent nodes represent m {\displaystyle m} Boolean variables

Annotation 1739184540940

#linear-algebra

In mathematics, more specifically in abstract algebra and linear algebra, a bilinear form on a vector space V is a bilinear map V × V → K , where K is the field of scalars.

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In mathematics, more specifically in abstract algebra and linear algebra, a bilinear form on a vector space V is a bilinear map V × V → K , where K is the field of scalars. In other words, a bilinear form is a function B : V × V → K that is linear in each argument separately: B(u + v, w) = B(u, w) + B(v, w) and B(λu, v) = λB(u, v) B(u, v + w) = B(u, v) +

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#linear-algebra

Question

a bilinear form on a vector space V is a bilinear map [...] ,

Answer

V × V → K

K is the field of scalars.
An inner product is obviously a bilinear form

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In mathematics, more specifically in abstract algebra and linear algebra, a bilinear form on a vector space V is a bilinear map V × V → K , where K is the field of scalars.

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#linear-algebra

Question

a bilinear form on a vector space V is a bilinear map V × V → K , where K is [...]

Answer

the field of scalars.

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In mathematics, more specifically in abstract algebra and linear algebra, a bilinear form on a vector space V is a bilinear map V × V → K , where K is the field of scalars.

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#probability-measure

Question

Compared to the more general notion of measure, a probability measure must assign value 1 to [...].

Answer

the entire probability space

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The difference between a probability measure and the more general notion of measure (which includes concepts like area or volume) is that a probability measure must assign value 1 to the entire probability space.

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Probability measure - Wikipedia
inequality Venn diagram Tree diagram v t e In mathematics, a probability measure is a real-valued function defined on a set of events in a probability space that satisfies measure properties such as countable additivity. [3] The difference between a probability measure and the more general notion of measure (which includes concepts like area or volume) is that a probability measure must assign value 1 to the entire probability space. Intuitively, the additivity property says that the probability assigned to the union of two disjoint events by the measure should be the sum of the probabilities of the events, e.g. t

Annotation 1741818825996

#functional-analysis

In mathematics, the support of a real-valued function f is the subset of the domain containing those elements which are not mapped to zero.

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Support (mathematics) - Wikipedia
eds additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (November 2009) (Learn how and when to remove this template message) In mathematics, the support of a real-valued function f is the subset of the domain containing those elements which are not mapped to zero. If the domain of f is a topological space, the support of f is instead defined as the smallest closed set containing all points not mapped to zero. This concept is used very widely in m

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#functional-analysis

Question

In mathematics, the support of a real-valued function f is the subset of the domain containing those elements which are [...]

Answer

not mapped to zero.

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In mathematics, the support of a real-valued function f is the subset of the domain containing those elements which are not mapped to zero.

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#functional-analysis

Question

In mathematics, the [...] of a real-valued function f is the subset of the domain containing those elements which are not mapped to zero.

Answer

support

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In mathematics, the support of a real-valued function f is the subset of the domain containing those elements which are not mapped to zero.

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#vector-space

Question

A norm must also satisfy certain properties pertaining to [...property...]

Answer

scalability and additivity

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A norm must also satisfy certain properties pertaining to scalability and additivity which are given in the formal definition below.

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Norm (mathematics) - Wikipedia
ositive length or size to each vector in a vector space—save for the zero vector, which is assigned a length of zero. A seminorm, on the other hand, is allowed to assign zero length to some non-zero vectors (in addition to the zero vector). A norm must also satisfy certain properties pertaining to scalability and additivity which are given in the formal definition below. A simple example is two dimensional Euclidean space R 2 equipped with the "Euclidean norm" (see below) Elements in this vector space (e.g., (3, 7)) are usually drawn as arr

Annotation 1744187821324

#spanish

El entrenador de Manchester United cree que no hay "mucho entusiasmo" de la hinchada, aunque los futbolistas "les gusta jugar" en casa.

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Noticias, Estadísticas y Resultados de Premiership de Inglaterra - ESPNDEPORTES - ESPNDeportes
[imagelink] 1dESPN Estadísticas e Información Kane llega a 100 goles en Premier League El goleador del Tottenham se reivindicó con ese tanto luego de fallar un penalti. [imagelink]play0:17 17h Mou criticó el ambiente tranquilo de Old Trafford El entrenador de Manchester United cree que no hay "mucho entusiasmo" de la hinchada, aunque los futbolistas "les gusta jugar" en casa. [imagelink]play José Mourinho y el gol 'no soñado' de Alexis Sánchez (0:17) [imagelink]play Pep Guardiola insiste: 'No quiero a nadie en Manchester' (0:45) Prem Posiciones EQUIPO PJ

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#optimal-control

Question

Optimal control finds a control law for a given system such that a certain [...] is achieved.

Answer

optimality criterion

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Optimal control deals with the problem of finding a control law for a given system such that a certain optimality criterion is achieved.

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Optimal control - Wikipedia
1 General method 2 Linear quadratic control 3 Numerical methods for optimal control 4 Discrete-time optimal control 5 Examples 5.1 Finite time 6 See also 7 References 8 Further reading 9 External links General method[edit source] Optimal control deals with the problem of finding a control law for a given system such that a certain optimality criterion is achieved. A control problem includes a cost functional that is a function of state and control variables. An optimal control is a set of differential equations describing the paths of the control

Annotation 1749121633548

#matrices #spectral-theorem

a spectral theorem is a result about when a linear operator or matrix can be diagonalized

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#matrices #spectral-theorem

Question

a spectral theorem is a result about when [...]

Answer

a linear operator or matrix can be diagonalized

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a spectral theorem is a result about when a linear operator or matrix can be diagonalized

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#inner-product-space

In a normed space, the statement of the parallelogram law is an equation relating norms:

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Parallelogram law - Wikipedia
2 {\displaystyle BD^{2}+AC^{2}=2a^{2}+2b^{2}} Q.E.D. The parallelogram law in inner product spaces[edit source] [imagelink] Vectors involved in the parallelogram law. In a normed space, the statement of the parallelogram law is an equation relating norms: 2 ‖ x ‖ 2 + 2 ‖ y ‖

Flashcard 1752701472012

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#inner-product-space

Question

In a normed space, the statement of the parallelogram law is [...]:

Answer

an equation relating norms

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In a normed space, the statement of the parallelogram law is an equation relating norms:

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#linear-algebra

a linear map is operation preserving: it does not matter whether you apply the linear map before or after the operations of addition and scalar multiplication.

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Linear map - Wikipedia
u ) = c f ( u ) {\displaystyle f(c\mathbf {u} )=cf(\mathbf {u} )} homogeneity of degree 1 / operation of scalar multiplication Thus, a linear map is said to be operation preserving. In other words, it does not matter whether you apply the linear map before or after the operations of addition and scalar multiplication. This is equivalent to requiring the same for any linear combination of vectors, i.e. that for any vectors u

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#linear-algebra

Question

a linear map is [...]: it does not matter whether you apply the linear map before or after the operations of addition and scalar multiplication.

Answer

operation preserving

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a linear map is operation preserving: it does not matter whether you apply the linear map before or after the operations of addition and scalar multiplication.

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#matrices #spectral-theorem

The spectral theorem provides a spectral decomposition of the underlying vector space on which the operator acts.

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Spectral theorem - Wikipedia
a statement about commutative C*-algebras. See also spectral theory for a historical perspective. Examples of operators to which the spectral theorem applies are self-adjoint operators or more generally normal operators on Hilbert spaces. The spectral theorem also provides a canonical decomposition, called the spectral decomposition, eigenvalue decomposition, or eigendecomposition, of the underlying vector space on which the operator acts. Augustin-Louis Cauchy proved the spectral theorem for self-adjoint matrices, i.e., that every real, symmetric matrix is diagonalizable. In addition, Cauchy was the first to be systema

Flashcard 1759683153164

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#matrices #spectral-theorem

Question

The spectral theorem provides a [...] of the underlying vector space on which the operator acts.

Answer

spectral decomposition

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The spectral theorem provides a spectral decomposition of the underlying vector space on which the operator acts.

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#spanish

El hijo de Drogba ficha por el Guingamp siguiendo los pasos de su padre

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Unknown title
ombates UFC Deportes Aventura eSports Juegos Olímpicos Olimpismo Paralímpicos Rugby Toros Turf Volvo Ocean Race Ligue 1 - Francia Liga FrancesaIsaac se formó en el Chelsea y ahora ficha por otro exequipo de Didier El hijo de Drogba ficha por el Guingamp siguiendo los pasos de su padre Compartir en Facebook Compartir en Twitter Enviar por email 20/02/2018 16:06 CET Isaac Drogba, durante su presentación con el Guingamp. 3 comentarios Comentar Guardiola vuelve a sa

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#spanish

Question

El hijo de Drogba [...] por el Guingamp siguiendo los pasos de su padre

Answer

ficha

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El hijo de Drogba ficha por el Guingamp siguiendo los pasos de su padre

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#politics

Atrocity propaganda is the spreading information about the crimes committed by an enemy, especially deliberate fabrications or exaggerations.

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Atrocity propaganda - Wikipedia
[imagelink] Atrocity propaganda From Wikipedia, the free encyclopedia Jump to: navigation, search Atrocity propaganda is the spreading information about the crimes committed by an enemy, especially deliberate fabrications or exaggerations. [citation needed] It is a form of psychological warfare. [citation needed] The inherently violent nature of war means that exaggeration and invention of atrocities often becomes the

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#politics

Question

[...] is the spread of information about the crimes committed by an enemy, especially deliberate fabrications or exaggerations.

Answer

Atrocity propaganda

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Atrocity propaganda is the spreading information about the crimes committed by an enemy, especially deliberate fabrications or exaggerations.

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#politics

Question

Atrocity propaganda is the spreading information about the crimes committed by an enemy, especially deliberate [...]

Answer

fabrications or exaggerations.

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Atrocity propaganda is the spreading information about the crimes committed by an enemy, especially deliberate fabrications or exaggerations.

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#rome

The Roman Kingdom, or regal period, was the period of the ancient Roman civilization characterized by a monarchical form of government of the city of Rome and its territories.

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Roman Kingdom - Wikipedia
Roman law Ius Imperium Mos maiorum Collegiality Auctoritas Roman citizenship Cursus honorum Senatus consultum Senatus consultum ultimum Assemblies Centuriate Curiate Plebeian Tribal Other countries Atlas v t e The Roman Kingdom, or regal period, was the period of the ancient Roman civilization characterized by a monarchical form of government of the city of Rome and its territories. Little is certain about the history of the kingdom, as nearly no written records from that time survive, and the histories about it that were written during the Republic and Empire ar

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#rome

Question

The [...] was the period of the ancient Roman civilization characterized by a monarchical form of government

Answer

Roman Kingdom

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The Roman Kingdom, or regal period, was the period of the ancient Roman civilization characterized by a monarchical form of government of the city of Rome and its territories. </h

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#hilbert-space

Question

The basic feature of the dot product that connects it with Euclidean geometry is that it is related to both [...] and [...]

Answer

length and angle

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The basic feature of the dot product that connects it with Euclidean geometry is that it is related to both the length of a vector, denoted || x || , and to the angle θ between two vectors x and y by means of the formula

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Hilbert space - Wikipedia
t product, satisfies these three properties is known as a (real) inner product. A vector space equipped with such an inner product is known as a (real) inner product space. Every finite-dimensional inner product space is also a Hilbert space. The basic feature of the dot product that connects it with Euclidean geometry is that it is related to both the length (or norm) of a vector, denoted ||x||, and to the angle θ between two vectors x and y by means of the formula x ⋅ y = ‖ x ‖ ‖ y ‖ cos ⁡ θ . {\displaystyle \mathbf {x} \cdot \mathbf {y} =\|\mathbf {x} \|\,\|\mathbf {y} \|\,\cos \theta \,.} [imagelink] Completeness means that if a particle moves along the broken path (in blue) travelling a finite total distance, then the particle has a well-defined net displacem

Flashcard 1802551823628

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#topology

Question

any [...] is equivalent to a linear transformation (of position vectors) followed by a translation.

Answer

affine transformation

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any affine transformation is equivalent to a linear transformation (of position vectors) followed by a translation.

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Affine transformation - Wikipedia
es in Euclidean spaces, each output coordinate of an affine map is a linear function (in the sense of calculus) of all input coordinates. Another way to deal with affine transformations systematically is to select a point as the origin; then, any affine transformation is equivalent to a linear transformation (of position vectors) followed by a translation. Contents [hide] 1 Mathematical definition 1.1 Alternative definition 2 Representation 2.1 Augmented matrix 2.1.1 Example augmented matrix 3 Properties 3.1 Properti

Flashcard 1802553396492

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#topology

Question

any affine transformation is equivalent to a [...] followed by a translation.

Answer

linear transformation (of position vectors)

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any affine transformation is equivalent to a linear transformation (of position vectors) followed by a translation.

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#topology

Question

any affine transformation is equivalent to a linear transformation (of position vectors) followed by a [...].

Answer

translation

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any affine transformation is equivalent to a linear transformation (of position vectors) followed by a translation.

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#functional-analysis

a functional equation is any equation in which the unknown represents a function.

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Functional equation - Wikipedia
Functional equation - Wikipedia Functional equation From Wikipedia, the free encyclopedia Jump to: navigation, search In mathematics, a functional equation [1] [2] [3] [4] is any equation in which the unknown represents a function. Often, the equation relates the value of a function (or functions) at some point with its values at other points. For instance, properties of functions can be determined by considering

Flashcard 1802561522956

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#functional-analysis

Question

a [...] is any equation in which the unknown represents a function.

Answer

functional equation

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a functional equation is any equation in which the unknown represents a function.

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#functional-analysis

Question

a functional equation is any equation in which [...].

Answer

the unknown represents a function

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a functional equation is any equation in which the unknown represents a function.

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#functional-analysis

A differential equation relates some function with its derivatives.

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Differential equation - Wikipedia
[imagelink] Visualization of heat transfer in a pump casing, created by solving the heat equation. Heat is being generated internally in the casing and being cooled at the boundary, providing a steady state temperature distribution. A differential equation is a mathematical equation that relates some function with its derivatives. In applications, the functions usually represent physical quantities, the derivatives represent their rates of change, and the equation defines a relationship between the two. Because s

Flashcard 1802569649420

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#functional-analysis

Question

A [...] relates some function with its derivatives.

Answer

differential equation

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A differential equation relates some function with its derivatives.

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#real-analysis

real analysis is the theory of real numbers and real functions, which are real-valued functions of a real variable. It is thus a branch of mathematical analysis, and deals, in particular, with the properties of limits, continuity, differentiability and integrability of these functions.

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Real analysis - Wikipedia
ncyclopedia Jump to: navigation, search [imagelink] The first four partial sums of the Fourier series for a square wave. Fourier series are an important tool in real analysis. In mathematics, real analysis is the theory of real numbers and real functions, which are real-valued functions of a real variable. It is thus a branch of mathematical analysis, and deals, in particular, with the properties of limits, continuity, differentiability and integrability of these functions. Contents [hide] 1 Scope 1.1 Construction of the real numbers 1.2 Order properties of the real numbers 1.3 Sequences 1.4 Limits and convergence 1.5 Continuity 1.5.1 Uniform

Flashcard 1802575940876

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#functional-analysis

Question

[...] studies

vector spaces that are endowed with some kind of limit-related structure and
the linear functions defined on these spaces and respecting these structures in a suitable sense.

Answer

Functional analysis

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Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. inner product, norm, topology, et

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Functional analysis - Wikipedia
analysis (psychology). [imagelink] One of the possible modes of vibration of an idealized circular drum head. These modes are eigenfunctions of a linear operator on a function space, a common construction in functional analysis. Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. inner product, norm, topology, etc.) and the linear functions defined on these spaces and respecting these structures in a suitable sense. The historical roots of functional analysis lie in the study of spaces of functions and the formulation of properties of transformations of functions such as the Fourier transform as transformations defining continuous, unitary etc. operators between function spaces. This point of view turned out to be particularly useful for the study of differential and integral equations. The usage of the word functional goes back to the calculus of variations, implying a function whose argument is a function and the name was first used in Hadamard's 1910 book on that

Flashcard 1802578300172

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#real-analysis

Question

[...]

studies the theory of real numbers and real functions and
deals with the properties of limits, continuity, differentiability and integrability of these functions.

Answer

real analysis

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real analysis is the theory of real numbers and real functions, which are real-valued functions of a real variable. It is thus a branch of mathematical analysis, and deals, in particular, with the pr

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#functional-analysis

The historical roots of functional analysis lie in the study of spaces of functions and transformations of functions

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f which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. inner product, norm, topology, etc.) and the linear functions defined on these spaces and respecting these structures in a suitable sense. The historical roots of functional analysis lie in the study of spaces of functions and the formulation of properties of transformations of functions such as the Fourier transform as transformations defining continuous, unitary etc. operators between function spaces. This point of view turned out to be particularly useful for the stu

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Annotation 1802582232332

#functional-analysis

linear operators are transformations of functions between function spaces

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spaces and respecting these structures in a suitable sense. The historical roots of functional analysis lie in the study of spaces of functions and the formulation of properties of transformations of functions such as the Fourier transform as transformations defining continuous, unitary etc. operators between function spaces. This point of view turned out to be particularly useful for the study of differential and integral equations. <body><html>

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Annotation 1802583805196

#functional-analysis

both differential and integral equations can be understand as linear operations on functions.

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unctional analysis lie in the study of spaces of functions and the formulation of properties of transformations of functions such as the Fourier transform as transformations defining continuous, unitary etc. operators between function spaces. This point of view turned out to be particularly useful for the study of differential and integral equations. <body><html>

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Flashcard 1802586164492

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#functional-analysis

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The historical roots of functional analysis lie in the study of [...and...]

Answer

spaces of functions and transformations of functions

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The historical roots of functional analysis lie in the study of spaces of functions and transformations of functions

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Flashcard 1802589310220

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#functional-analysis

Question

[...] are transformations of functions between function spaces

Answer

linear operators

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linear operators are transformations of functions between function spaces

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Flashcard 1802591669516

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#functional-analysis

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both differential and integral equations can be understand as [...] on functions.

Answer

linear operations

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both differential and integral equations can be understand as linear operations on functions.

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Flashcard 1802638069004

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#French

Question

On the A and U [...] usually serves to distinguish between words that would otherwise be identical

Answer

grave accent `

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The "accent grave" ` (grave accent) can be on an A, E, or U. On the A and U, it usually serves to distinguish between words that would otherwise be written the same, ex: ou (or) vs où (where), "a" (has) vs "à" (to, at)

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Duolingo: Learn Spanish, French and other languages for free
low discussion Topic: French [imagelink] Accents in French Remy 19 14 13 11 11 6 4 665 In French, there are 4 accents for vowels and 1 accent for a consonant. The "accent aigu" ´ (acute accent) can only be on an E. The "accent grave" ` (grave accent) can be on an A, E, or U. On the A and U, it usually serves to distinguish between words that would otherwise be written the same, ex: ou (or) vs où (where), "a" (has) vs "à" (to, at) The "accent circonflexe" ˆ (circumflex) can be on an A, E, I, O, or U. In general, it indicates that an S used to follow that vowel, e.g., forêt (forest). The "accent

Annotation 1802640428300

#French

The "accent tréma" ¨ (dieresis or umlaut) can be on an E, I, or U. It is used when two vowels are next to each other and both must be pronounced, ex: maïs.

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Duolingo: Learn Spanish, French and other languages for free
ex: ou (or) vs où (where), "a" (has) vs "à" (to, at) The "accent circonflexe" ˆ (circumflex) can be on an A, E, I, O, or U. In general, it indicates that an S used to follow that vowel, e.g., forêt (forest). The "accent tréma" ¨ (dieresis or umlaut) can be on an E, I, or U. It is used when two vowels are next to each other and both must be pronounced, ex: maïs. The "cédille" ¸ (cedilla) is found only on the letter C. It changes a hard C sound (like K) into a soft C sound (like S), e.g., garçon. It never appears in front of E or I,

Annotation 1802642001164

#French

The "accent circonflexe" ˆ (circumflex) can be on an A, E, I, O, or U. In general, it indicates that an S used to follow that vowel, e.g., forêt (forest).

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Duolingo: Learn Spanish, French and other languages for free
t;accent grave" ` (grave accent) can be on an A, E, or U. On the A and U, it usually serves to distinguish between words that would otherwise be written the same, ex: ou (or) vs où (where), "a" (has) vs "à" (to, at) The "accent circonflexe" ˆ (circumflex) can be on an A, E, I, O, or U. In general, it indicates that an S used to follow that vowel, e.g., forêt (forest). The "accent tréma" ¨ (dieresis or umlaut) can be on an E, I, or U. It is used when two vowels are next to each other and both must be pronounced, ex: maïs. The "cédil

Flashcard 1802643574028

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#French

Question

[...] is used when two vowels are next to each other and both must be pronounced

Answer

umlaut ¨

ex: maïs.

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The "accent tréma" ¨ (dieresis or umlaut) can be on an E, I, or U. It is used when two vowels are next to each other and both must be pronounced, ex: maïs.

Original toplevel document

Flashcard 1802645933324

Tags

#French

Question

[...] usually indicates that an S used to follow that vowel

Answer

circumflex ˆ

e.g., forêt (forest).

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The "accent circonflexe" ˆ (circumflex) can be on an A, E, I, O, or U. In general, it indicates that an S used to follow that vowel, e.g., forêt (forest).

Edited, memorised or added to reading queue

on 22-Apr-2018 (Sun)

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