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Wikipedia:FAQ - Wikipedia, the free encyclopedia
cal, legal, financial, safety, and other critical issues? 8 Who owns Wikipedia? 9 Why am I having trouble logging in? 10 How can I contact Wikipedia? How do I create a new page? <span>You are required to have a Wikipedia account to create a new article—you can register here. To see other benefits to creating an account, see Why create an account? For creating a new article see Wikipedia:Your first article and Wikipedia:Article development; and you may wi




Flashcard 1438666853644

Tags
#cfa-level-1 #corporate-finance #reading-35-capital-budgeting #study-session-10
Question
opportunity cost.

If a company uses some idle property, what should it record as the investment outlay: the purchase price several years ago, the current market value, or nothing?
Answer
Market Value


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3. BASIC PRINCIPLES OF CAPITAL BUDGETING
A sunk cost is one that has already been incurred. You cannot change a sunk cost. Today’s decisions, on the other hand, should be based on current and future cash flows and should not be affected by prior, or sunk, costs. <span>An opportunity cost is what a resource is worth in its next-best use. For example, if a company uses some idle property, what should it record as the investment outlay: the purchase price several years ago, the current market value, or nothing? If you replace an old machine with a new one, what is the opportunity cost? If you invest $10 million, what is the opportunity cost? The answers to these three questions are, respective







Flashcard 1457029778700

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#48-laws-of-power
Question
LAW 3 [...]
Answer
CONCEAL YOUR INTENTIONS


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LAW 3 CONCEAL YOUR INTENTIONS JUDGMENT Keep people off-balance and in the dark by never revealing the purpose behind your actions. If they have no clue what you are up to, they cannot prepare a defense. Guide them f

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Flashcard 1477033725196

Question
“IF YOU WANT TO GATHER HONEY, [...]
Answer
DON’T KICK OVER THE BEEHIVE


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“IF YOU WANT TO GATHER HONEY, DON’T KICK OVER THE BEEHIVE

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the biggest profits are to be made when you buy low and sell high

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make money repositioning multi-family properties.

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the right strategy for the particular phase a market is in to maximize your profits

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There are four different phases of a market cycle. Some strategies will work great in one phase, while others will not work at all—until perhaps the next phase, when they’ll be just the right ones to use.

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I’ll show you how to get the very most done in the shortest possible time. I’m a time fanatic, and you’re going to benefit from that.

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it will take more than one deal to reach financial freedom.

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if you will do for three to five years what most people won’t do, then you can do for the rest of your life what most people can’t do.

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follow the rules and steps in the order I give them

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The more properties you can control with the least amount of money out of your pocket, the faster you will become wealthy.

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I began to fund my own deals and didn’t need to get into deals with no money down, because now I had money!

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Eventually—no matter how rich you are—you will run out of money to do all the deals you want to do. You will need to use other people’s money to fund at least some of those deals.

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if you always use your own money to get into a deal, you live your life in a feast-or-famine cycle. You feast after you sell a property and get a chunk of cash, but more often than not, you are in famine mode while your money is tied up in properties that are getting ready for sale or refinance.

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Us- ing other people’s money wisely means you can avoid this cash-flow crunch.

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Banks usually do require you to put 20 to 30 percent down on property.

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many options for finding all the money you need.

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T here are a great many different ways to invest in real estate: Just within the area of single-family homes, you can buy and sell through wholesaling, retailing, lease options, and subject to. You can specialize in foreclosures, abandoned houses, fixer- uppers, and pretty houses. Then there are techniques for investing in shopping centers, land, warehouses, industrial properties, and office buildings.

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apartment buildings. They can be big (400-plus units) or small (two to six units). Regardless of the size you buy, start buying them!

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You do not have to be the stereotypical landlord to enjoy the profits from an apartment building. A qualified property manager does all the hard work. They take care of the tenants, collect the rents, pay the bills, pay the mortgage, and put a chunk of cash flow into Robert’s bank account every month.

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big numbers rep- resents a number of apartment units. Once you’ve accumulated that number of units, you’re done. You are done for the rest of your life

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#dual-space
In mathematics, any vector space V has a corresponding dual vector space consisting of all linear functionals on V, together with the vector space structure of pointwise addition and scalar multiplication by constants.

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Dual space - Wikipedia
Dual space - Wikipedia Dual space From Wikipedia, the free encyclopedia Jump to: navigation, search In mathematics, any vector space V has a corresponding dual vector space (or just dual space for short) consisting of all linear functionals on V, together with the vector space structure of pointwise addition and scalar multiplication by constants. The dual space as defined above is defined for all vector spaces, and to avoid ambiguity may also be called the algebraic dual space. When defined for a topological vector space, ther




Flashcard 1759615257868

Tags
#dual-space
Question
A dual vector space has the vector space structure of [...].
Answer
pointwise addition and scalar multiplication by constants


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In mathematics, any vector space V has a corresponding dual vector space consisting of all linear functionals on V, together with the vector space structure of pointwise addition and scalar multiplication by constants.

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Dual space - Wikipedia
Dual space - Wikipedia Dual space From Wikipedia, the free encyclopedia Jump to: navigation, search In mathematics, any vector space V has a corresponding dual vector space (or just dual space for short) consisting of all linear functionals on V, together with the vector space structure of pointwise addition and scalar multiplication by constants. The dual space as defined above is defined for all vector spaces, and to avoid ambiguity may also be called the algebraic dual space. When defined for a topological vector space, ther







#hilbert-space
At a deeper level, perpendicular projection onto a subspace plays a significant role in optimization problems and other aspects of the theory.

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Hilbert space - Wikipedia
f generalized functions, and Hardy spaces of holomorphic functions. Geometric intuition plays an important role in many aspects of Hilbert space theory. Exact analogs of the Pythagorean theorem and parallelogram law hold in a Hilbert space. <span>At a deeper level, perpendicular projection onto a subspace (the analog of "dropping the altitude" of a triangle) plays a significant role in optimization problems and other aspects of the theory. An element of a Hilbert space can be uniquely specified by its coordinates with respect to a set of coordinate axes (an orthonormal basis), in analogy with Cartesian coordinates in the




#hilbert-space
When that set of axes is countably infinite, the Hilbert space can also be usefully thought of in terms of the space of infinite sequences that are square-summable.

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Hilbert space - Wikipedia
mization problems and other aspects of the theory. An element of a Hilbert space can be uniquely specified by its coordinates with respect to a set of coordinate axes (an orthonormal basis), in analogy with Cartesian coordinates in the plane. <span>When that set of axes is countably infinite, the Hilbert space can also be usefully thought of in terms of the space of infinite sequences that are square-summable. The latter space is often in the older literature referred to as the Hilbert space. Linear operators on a Hilbert space are likewise fairly concrete objects: in good cases, they are sim




#hilbert-space
Every finite-dimensional inner product space is also a Hilbert space.

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Hilbert space - Wikipedia
nd only if x = 0. An operation on pairs of vectors that, like the dot 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. <span>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 t




#calculus
In mathematics, an infinite series of numbers is said to converge absolutely if the sum of the absolute values of the summands is finite.

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Absolute convergence - Wikipedia
of references, but its sources remain unclear because it has insufficient inline citations. Please help to improve this article by introducing more precise citations. (February 2013) (Learn how and when to remove this template message) <span>In mathematics, an infinite series of numbers is said to converge absolutely (or to be absolutely convergent) if the sum of the absolute values of the summands is finite. More precisely, a real or complex series ∑ n = 0




#hilbert-space
This inner product in the space ℂ2 is Hermitian symmetric, which means that the result of interchanging z and w is the complex conjugate:

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Hilbert space - Wikipedia
2 . {\displaystyle \langle z,w\rangle =z_{1}{\overline {w}}_{1}+z_{2}{\overline {w}}_{2}\,.} The real part of ⟨z,w⟩ is then the four-dimensional Euclidean dot product. <span>This inner product is Hermitian symmetric, which means that the result of interchanging z and w is the complex conjugate: ⟨ w , z ⟩ = ⟨ z , w




#hilbert-space

Hilbert spaces are the natural abstract framework in which to study two important (and closely related) concepts: orthogonality and unitarity, allowing us to generalise familiar concepts and facts from Euclidean geometry such as the Cartesian coordinate system, rotations and reflections, and the Pythagorean theorem to Hilbert spaces. (For instance, the Fourier transform is a unitary transformation and can thus be viewed as a kind of generalised rotation.) Furthermore, the Hodge duality on Euclidean spaces has a partial analogue for Hilbert spaces, namely the Riesz representation theorem for Hilbert spaces, which makes the theory of duality and adjoints for Hilbert spaces especially simple (when compared with the more subtle theory of duality for, say, Banach spaces). Much later (next quarter, in fact), we will see that this duality allows us to extend the spectral theorem for self-adjoint matrices to that of self-adjoint operators on a Hilbert space.

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245B, notes 5: Hilbert spaces | What's new
also play a fundamental role in the foundations of quantum mechanics, being the natural space to hold all the possible states of a quantum system (possibly after projectivising the Hilbert space), but we will not discuss this subject here.) <span>Hilbert spaces are the natural abstract framework in which to study two important (and closely related) concepts: orthogonality and unitarity, allowing us to generalise familiar concepts and facts from Euclidean geometry such as the Cartesian coordinate system, rotations and reflections, and the Pythagorean theorem to Hilbert spaces. (For instance, the Fourier transform is a unitary transformation and can thus be viewed as a kind of generalised rotation.) Furthermore, the Hodge duality on Euclidean spaces has a partial analogue for Hilbert spaces, namely the Riesz representation theorem for Hilbert spaces, which makes the theory of duality and adjoints for Hilbert spaces especially simple (when compared with the more subtle theory of duality for, say, Banach spaces). Much later (next quarter, in fact), we will see that this duality allows us to extend the spectral theorem for self-adjoint matrices to that of self-adjoint operators on a Hilbert space. These notes are only the most basic introduction to the theory of Hilbert spaces. In particular, the theory of linear transformations between two Hilbert spaces, which is perhaps the




#inner-product-space

The Cauchy–Schwarz inequality states that for all vectors and of an inner product space it is true that

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Cauchy–Schwarz inequality - Wikipedia
al space) 3.2 R n (n-dimensional Euclidean space) 3.3 L 2 4 Applications 4.1 Analysis 4.2 Geometry 4.3 Probability theory 5 Generalizations 6 See also 7 Notes 8 References 9 External links Statement of the inequality[edit source] <span>The Cauchy–Schwarz inequality states that for all vectors u {\displaystyle u} and v {\displaystyle v} of an inner product space it is true that | ⟨ u , v ⟩ | 2 ≤ ⟨ u , u ⟩ ⋅ ⟨ v , v ⟩ , {\displaystyle |\langle \mathbf {u} ,\mathbf {v} \rangle |^{2}\leq \langle \mathbf {u} ,\mathbf {u} \rangle \cdot \langle \mathbf {v} ,\mathbf {v} \rangle ,} where ⟨ ⋅ , ⋅ ⟩ {\displaystyle \langle \cdot ,\cdot \rangle } is the inner product. Examples of inner products include the real and complex dot product, see the examples in inner product. Equivalently, by taking the square root of both sides, and referring to the norms




#hilbert-space
This last property is ultimately a consequence of the more fundamental Cauchy–Schwarz inequality

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Hilbert space - Wikipedia
) ≤ d ( x , y ) + d ( y , z ) . {\displaystyle d(x,z)\leq d(x,y)+d(y,z)\,.} [imagelink] <span>This last property is ultimately a consequence of the more fundamental Cauchy–Schwarz inequality, which asserts | ⟨ x , y ⟩ |




#functional-analysis
In functional analysis and related areas of mathematics, a sequence space is a vector space whose elements are infinite sequences of real or complex numbers

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Sequence space - Wikipedia
a, the free encyclopedia Jump to: navigation, search For usage in evolutionary biology, see Sequence space (evolution). For mathematical operations on sequence numbers, see Serial number arithmetic. <span>In functional analysis and related areas of mathematics, a sequence space is a vector space whose elements are infinite sequences of real or complex numbers. Equivalently, it is a function space whose elements are functions from the natural numbers to the field K of real or complex numbers. The set of all such functions is naturally identif




#vector-space

Let p ≥ 1 be a real number. The -norm of vectors is

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Norm (mathematics) - Wikipedia
x i {\displaystyle \sum _{i=1}^{n}x_{i}} is not a norm because it may yield negative results. p-norm[edit source] Main article: L p space <span>Let p ≥ 1 be a real number. The p {\displaystyle p} -norm (also called ℓ p {\displaystyle \ell _{p}} -norm) of vectors x = ( x 1 , … , x n ) {\displaystyle \mathbf {x} =(x_{1},\ldots ,x_{n})} is ‖ x ‖ p := ( ∑ i = 1 n | x i | p ) 1 / p . {\displaystyle \left\|\mathbf {x} \right\|_{p}:={\bigg (}\sum _{i=1}^{n}\left|x_{i}\right|^{p}{\bigg )}^{1/p}.} For p = 1 we get the taxicab norm, for p = 2 we get the Euclidean norm, and as p approaches ∞ {\displaystyle \infty } the p-norm approa




Flashcard 1759650385164

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#vector-space
Question

Let p ≥ 1 be a real number. The -norm of vectors is [...]

Answer


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Let p ≥ 1 be a real number. The -norm of vectors is

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Norm (mathematics) - Wikipedia
x i {\displaystyle \sum _{i=1}^{n}x_{i}} is not a norm because it may yield negative results. p-norm[edit source] Main article: L p space <span>Let p ≥ 1 be a real number. The p {\displaystyle p} -norm (also called ℓ p {\displaystyle \ell _{p}} -norm) of vectors x = ( x 1 , … , x n ) {\displaystyle \mathbf {x} =(x_{1},\ldots ,x_{n})} is ‖ x ‖ p := ( ∑ i = 1 n | x i | p ) 1 / p . {\displaystyle \left\|\mathbf {x} \right\|_{p}:={\bigg (}\sum _{i=1}^{n}\left|x_{i}\right|^{p}{\bigg )}^{1/p}.} For p = 1 we get the taxicab norm, for p = 2 we get the Euclidean norm, and as p approaches ∞ {\displaystyle \infty } the p-norm approa







Flashcard 1759652744460

Tags
#vector-space
Question

Let p ≥ 1 be a real number. The [...] of vectors is

Answer
-norm


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Let p ≥ 1 be a real number. The -norm of vectors is

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Norm (mathematics) - Wikipedia
x i {\displaystyle \sum _{i=1}^{n}x_{i}} is not a norm because it may yield negative results. p-norm[edit source] Main article: L p space <span>Let p ≥ 1 be a real number. The p {\displaystyle p} -norm (also called ℓ p {\displaystyle \ell _{p}} -norm) of vectors x = ( x 1 , … , x n ) {\displaystyle \mathbf {x} =(x_{1},\ldots ,x_{n})} is ‖ x ‖ p := ( ∑ i = 1 n | x i | p ) 1 / p . {\displaystyle \left\|\mathbf {x} \right\|_{p}:={\bigg (}\sum _{i=1}^{n}\left|x_{i}\right|^{p}{\bigg )}^{1/p}.} For p = 1 we get the taxicab norm, for p = 2 we get the Euclidean norm, and as p approaches ∞ {\displaystyle \infty } the p-norm approa







#lebesgue-space
In mathematics, the Lp spaces are function spaces defined using a natural generalization of the p-norm for finite-dimensional vector spaces. They are sometimes called Lebesgue spaces,

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Lp space - Wikipedia
Lp space - Wikipedia L p space From Wikipedia, the free encyclopedia Jump to: navigation, search In mathematics, the L p spaces are function spaces defined using a natural generalization of the p-norm for finite-dimensional vector spaces. They are sometimes called Lebesgue spaces, named after Henri Lebesgue (Dunford & Schwartz 1958, III.3), although according to the Bourbaki group (Bourbaki 1987) they were first introduced by Frigyes Riesz (Riesz 1910). L p




#lebesgue-space
In mathematics, the Lp spaces are function spaces defined using a natural generalization of the p-norm for finite-dimensional vector spaces.

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In mathematics, the L p spaces are function spaces defined using a natural generalization of the p-norm for finite-dimensional vector spaces. They are sometimes called Lebesgue spaces,

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Lp space - Wikipedia
Lp space - Wikipedia L p space From Wikipedia, the free encyclopedia Jump to: navigation, search In mathematics, the L p spaces are function spaces defined using a natural generalization of the p-norm for finite-dimensional vector spaces. They are sometimes called Lebesgue spaces, named after Henri Lebesgue (Dunford & Schwartz 1958, III.3), although according to the Bourbaki group (Bourbaki 1987) they were first introduced by Frigyes Riesz (Riesz 1910). L p




Flashcard 1759660870924

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#lebesgue-space
Question
Lebesgue spaces are sometimes called [...]
Answer
Lp spaces


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In mathematics, the L p spaces are function spaces defined using a natural generalization of the p-norm for finite-dimensional vector spaces. They are sometimes called Lebesgue spaces,

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Lp space - Wikipedia
Lp space - Wikipedia L p space From Wikipedia, the free encyclopedia Jump to: navigation, search In mathematics, the L p spaces are function spaces defined using a natural generalization of the p-norm for finite-dimensional vector spaces. They are sometimes called Lebesgue spaces, named after Henri Lebesgue (Dunford & Schwartz 1958, III.3), although according to the Bourbaki group (Bourbaki 1987) they were first introduced by Frigyes Riesz (Riesz 1910). L p







Flashcard 1759663230220

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#lebesgue-space
Question
Lp spaces are function spaces defined using a natural generalization of [...]
Answer
the p-norm for finite-dimensional vector spaces.


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In mathematics, the L p spaces are function spaces defined using a natural generalization of the p-norm for finite-dimensional vector spaces.

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Lp space - Wikipedia
Lp space - Wikipedia L p space From Wikipedia, the free encyclopedia Jump to: navigation, search In mathematics, the L p spaces are function spaces defined using a natural generalization of the p-norm for finite-dimensional vector spaces. They are sometimes called Lebesgue spaces, named after Henri Lebesgue (Dunford & Schwartz 1958, III.3), although according to the Bourbaki group (Bourbaki 1987) they were first introduced by Frigyes Riesz (Riesz 1910). L p







Flashcard 1759664803084

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#lebesgue-space
Question
In mathematics, the [...] are function spaces defined using a natural generalization of the p-norm for finite-dimensional vector spaces.
Answer
Lp spaces


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In mathematics, the L p spaces are function spaces defined using a natural generalization of the p-norm for finite-dimensional vector spaces.

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Lp space - Wikipedia
Lp space - Wikipedia L p space From Wikipedia, the free encyclopedia Jump to: navigation, search In mathematics, the L p spaces are function spaces defined using a natural generalization of the p-norm for finite-dimensional vector spaces. They are sometimes called Lebesgue spaces, named after Henri Lebesgue (Dunford & Schwartz 1958, III.3), although according to the Bourbaki group (Bourbaki 1987) they were first introduced by Frigyes Riesz (Riesz 1910). L p







Flashcard 1759666375948

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#functional-analysis
Question
a [...] is a vector space whose elements are infinite sequences
Answer
sequence space


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In functional analysis and related areas of mathematics, a sequence space is a vector space whose elements are infinite sequences of real or complex numbers

Original toplevel document

Sequence space - Wikipedia
a, the free encyclopedia Jump to: navigation, search For usage in evolutionary biology, see Sequence space (evolution). For mathematical operations on sequence numbers, see Serial number arithmetic. <span>In functional analysis and related areas of mathematics, a sequence space is a vector space whose elements are infinite sequences of real or complex numbers. Equivalently, it is a function space whose elements are functions from the natural numbers to the field K of real or complex numbers. The set of all such functions is naturally identif







Flashcard 1759667948812

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#functional-analysis
Question
a sequence space is a vector space whose elements are [...]
Answer


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In functional analysis and related areas of mathematics, a sequence space is a vector space whose elements are infinite sequences of real or complex numbers

Original toplevel document

Sequence space - Wikipedia
a, the free encyclopedia Jump to: navigation, search For usage in evolutionary biology, see Sequence space (evolution). For mathematical operations on sequence numbers, see Serial number arithmetic. <span>In functional analysis and related areas of mathematics, a sequence space is a vector space whose elements are infinite sequences of real or complex numbers. Equivalently, it is a function space whose elements are functions from the natural numbers to the field K of real or complex numbers. The set of all such functions is naturally identif







#spectral-analysis

In mathematics, an eigenfunction of a linear operator D defined on some function space is any non-zero function f in that space that for some scalar eigenvalue λ.

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Eigenfunction - Wikipedia
ected from Eigenfunction expansion) Jump to: navigation, search [imagelink] This solution of the vibrating drum problem is, at any point in time, an eigenfunction of the Laplace operator on a disk. <span>In mathematics, an eigenfunction of a linear operator D defined on some function space is any non-zero function f in that space that, when acted upon by D, is only multiplied by some scaling factor called an eigenvalue. As an equation, this condition can be written as D f = λ f {\displaystyle Df=\lambda f} for some scalar eigenvalue λ. [1] [2] [3] The solutions to this equation may also be subject to boundary conditions that limit the allowable eigenvalues and eigenfunctions. An eigenfunction is a type of eigenvect




Flashcard 1759676075276

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#spectral-analysis
Question

an eigenfunction of a linear operator D defined on some function space is any non-zero function f in that space that satisfies [...]

Answer
for some scalar eigenvalue λ.


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In mathematics, an eigenfunction of a linear operator D defined on some function space is any non-zero function f in that space that for some scalar eigenvalue λ.

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Eigenfunction - Wikipedia
ected from Eigenfunction expansion) Jump to: navigation, search [imagelink] This solution of the vibrating drum problem is, at any point in time, an eigenfunction of the Laplace operator on a disk. <span>In mathematics, an eigenfunction of a linear operator D defined on some function space is any non-zero function f in that space that, when acted upon by D, is only multiplied by some scaling factor called an eigenvalue. As an equation, this condition can be written as D f = λ f {\displaystyle Df=\lambda f} for some scalar eigenvalue λ. [1] [2] [3] The solutions to this equation may also be subject to boundary conditions that limit the allowable eigenvalues and eigenfunctions. An eigenfunction is a type of eigenvect







Flashcard 1759678434572

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#spectral-analysis
Question

In mathematics, [...] defined on some function space is any non-zero function f in that space that satisfies for some scalar eigenvalue λ.

Answer
an eigenfunction of a linear operator D


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In mathematics, an eigenfunction of a linear operator D defined on some function space is any non-zero function f in that space that for some scalar eigenvalue λ.

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Eigenfunction - Wikipedia
ected from Eigenfunction expansion) Jump to: navigation, search [imagelink] This solution of the vibrating drum problem is, at any point in time, an eigenfunction of the Laplace operator on a disk. <span>In mathematics, an eigenfunction of a linear operator D defined on some function space is any non-zero function f in that space that, when acted upon by D, is only multiplied by some scaling factor called an eigenvalue. As an equation, this condition can be written as D f = λ f {\displaystyle Df=\lambda f} for some scalar eigenvalue λ. [1] [2] [3] The solutions to this equation may also be subject to boundary conditions that limit the allowable eigenvalues and eigenfunctions. An eigenfunction is a type of eigenvect







#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. <span>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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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. <span>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







#integral-equation

In mathematics, an integral equation is an equation in which an unknown function appears under an integral sign.

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Integral equation - Wikipedia
Integral equation From Wikipedia, the free encyclopedia (Redirected from Integral equations) Jump to: navigation, search For equations of integer unknowns, see Diophantine equation. <span>In mathematics, an integral equation is an equation in which an unknown function appears under an integral sign. There is a close connection between differential and integral equations, and some problems may be formulated either way. See, for example, Green's function, Fredholm theory, and Maxwe




#integral-equation

The most basic type of integral equation is where φ is an unknown function,  f  is a known function, and K is another known function of two variables, often called the kernel function.

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Integral equation - Wikipedia
rview 2 Numerical solution 3 Classification 4 Wiener–Hopf integral equations 5 Power series solution for integral equations 6 Integral equations as a generalization of eigenvalue equations 7 See also 8 References 9 External links Overview<span>[edit source] The most basic type of integral equation is called a Fredholm equation of the first type, f ( x ) = ∫ a b K ( x , t ) φ ( t ) d t . {\displaystyle f(x)=\int _{a}^{b}K(x,t)\,\varphi (t)\,dt.} The notation follows Arfken. Here φ is an unknown function,  f  is a known function, and K is another known function of two variables, often called the kernel function. Note that the limits of integration are constant: this is what characterizes a Fredholm equation. If the unknown function occurs both inside and outside of the integral, the equation




Flashcard 1759689706764

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#integral-equation
Question

In mathematics, an integral equation is an equation in which [...]

Answer
an unknown function appears under an integral sign.


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In mathematics, an integral equation is an equation in which an unknown function appears under an integral sign.

Original toplevel document

Integral equation - Wikipedia
Integral equation From Wikipedia, the free encyclopedia (Redirected from Integral equations) Jump to: navigation, search For equations of integer unknowns, see Diophantine equation. <span>In mathematics, an integral equation is an equation in which an unknown function appears under an integral sign. There is a close connection between differential and integral equations, and some problems may be formulated either way. See, for example, Green's function, Fredholm theory, and Maxwe







Flashcard 1759692066060

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#integral-equation
Question

In mathematics, an [...] is an equation in which an unknown function appears under an integral sign.

Answer
integral equation


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In mathematics, an integral equation is an equation in which an unknown function appears under an integral sign.

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Integral equation - Wikipedia
Integral equation From Wikipedia, the free encyclopedia (Redirected from Integral equations) Jump to: navigation, search For equations of integer unknowns, see Diophantine equation. <span>In mathematics, an integral equation is an equation in which an unknown function appears under an integral sign. There is a close connection between differential and integral equations, and some problems may be formulated either way. See, for example, Green's function, Fredholm theory, and Maxwe







Flashcard 1759694425356

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#integral-equation
Question

The most basic type of integral equation is [...]

Answer


where φ is an unknown function,  f  is a known function, and K is another known function of two variables, often called the kernel function.


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The most basic type of integral equation is where φ is an unknown function,  f  is a known function, and K is another known function of two variables, often called the kernel function.

Original toplevel document

Integral equation - Wikipedia
rview 2 Numerical solution 3 Classification 4 Wiener–Hopf integral equations 5 Power series solution for integral equations 6 Integral equations as a generalization of eigenvalue equations 7 See also 8 References 9 External links Overview<span>[edit source] The most basic type of integral equation is called a Fredholm equation of the first type, f ( x ) = ∫ a b K ( x , t ) φ ( t ) d t . {\displaystyle f(x)=\int _{a}^{b}K(x,t)\,\varphi (t)\,dt.} The notation follows Arfken. Here φ is an unknown function,  f  is a known function, and K is another known function of two variables, often called the kernel function. Note that the limits of integration are constant: this is what characterizes a Fredholm equation. If the unknown function occurs both inside and outside of the integral, the equation







In mathematics, a square-integrable function is a real- or complex-valued measurable function for which the integral of the square of the absolute value is finite.

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Square-integrable function - Wikipedia
Square-integrable function - Wikipedia Square-integrable function From Wikipedia, the free encyclopedia (Redirected from Square-integrable) Jump to: navigation, search <span>In mathematics, a square-integrable function, also called a quadratically integrable function, is a real- or complex-valued measurable function for which the integral of the square of the absolute value is finite. Thus, if ∫ − ∞ ∞ | f




Flashcard 1759700978956

Question
In mathematics, a square-integrable function is a real- or complex-valued measurable function for which [...]
Answer
the integral of the square of the absolute value is finite.


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In mathematics, a square-integrable function is a real- or complex-valued measurable function for which the integral of the square of the absolute value is finite.

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Square-integrable function - Wikipedia
Square-integrable function - Wikipedia Square-integrable function From Wikipedia, the free encyclopedia (Redirected from Square-integrable) Jump to: navigation, search <span>In mathematics, a square-integrable function, also called a quadratically integrable function, is a real- or complex-valued measurable function for which the integral of the square of the absolute value is finite. Thus, if ∫ − ∞ ∞ | f







Flashcard 1759702551820

Question
In mathematics, a [...] is a real- or complex-valued measurable function for which the integral of the square of the absolute value is finite.
Answer
square-integrable function


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In mathematics, a square-integrable function is a real- or complex-valued measurable function for which the integral of the square of the absolute value is finite.

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Square-integrable function - Wikipedia
Square-integrable function - Wikipedia Square-integrable function From Wikipedia, the free encyclopedia (Redirected from Square-integrable) Jump to: navigation, search <span>In mathematics, a square-integrable function, also called a quadratically integrable function, is a real- or complex-valued measurable function for which the integral of the square of the absolute value is finite. Thus, if ∫ − ∞ ∞ | f







Flashcard 1759704911116

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#inner-product-space
Question

The [...] states that for all vectors and of an inner product space it is true that

Answer
Cauchy–Schwarz inequality


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The Cauchy–Schwarz inequality states that for all vectors and of an inner product space it is true that

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Cauchy–Schwarz inequality - Wikipedia
al space) 3.2 R n (n-dimensional Euclidean space) 3.3 L 2 4 Applications 4.1 Analysis 4.2 Geometry 4.3 Probability theory 5 Generalizations 6 See also 7 Notes 8 References 9 External links Statement of the inequality[edit source] <span>The Cauchy–Schwarz inequality states that for all vectors u {\displaystyle u} and v {\displaystyle v} of an inner product space it is true that | ⟨ u , v ⟩ | 2 ≤ ⟨ u , u ⟩ ⋅ ⟨ v , v ⟩ , {\displaystyle |\langle \mathbf {u} ,\mathbf {v} \rangle |^{2}\leq \langle \mathbf {u} ,\mathbf {u} \rangle \cdot \langle \mathbf {v} ,\mathbf {v} \rangle ,} where ⟨ ⋅ , ⋅ ⟩ {\displaystyle \langle \cdot ,\cdot \rangle } is the inner product. Examples of inner products include the real and complex dot product, see the examples in inner product. Equivalently, by taking the square root of both sides, and referring to the norms







Flashcard 1759706483980

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#inner-product-space
Question
The Cauchy–Schwarz inequality states that for all vectors and of an inner product space it is true that [...]
Answer


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The Cauchy–Schwarz inequality states that for all vectors and of an inner product space it is true that

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Cauchy–Schwarz inequality - Wikipedia
al space) 3.2 R n (n-dimensional Euclidean space) 3.3 L 2 4 Applications 4.1 Analysis 4.2 Geometry 4.3 Probability theory 5 Generalizations 6 See also 7 Notes 8 References 9 External links Statement of the inequality[edit source] <span>The Cauchy–Schwarz inequality states that for all vectors u {\displaystyle u} and v {\displaystyle v} of an inner product space it is true that | ⟨ u , v ⟩ | 2 ≤ ⟨ u , u ⟩ ⋅ ⟨ v , v ⟩ , {\displaystyle |\langle \mathbf {u} ,\mathbf {v} \rangle |^{2}\leq \langle \mathbf {u} ,\mathbf {u} \rangle \cdot \langle \mathbf {v} ,\mathbf {v} \rangle ,} where ⟨ ⋅ , ⋅ ⟩ {\displaystyle \langle \cdot ,\cdot \rangle } is the inner product. Examples of inner products include the real and complex dot product, see the examples in inner product. Equivalently, by taking the square root of both sides, and referring to the norms







Flashcard 1759708843276

Tags
#hilbert-space
Question
This inner product in the space ℂ2 is [...property...]
Answer
Hermitian symmetric


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This inner product in the space ℂ 2 is Hermitian symmetric, which means that the result of interchanging z and w is the complex conjugate:

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Hilbert space - Wikipedia
2 . {\displaystyle \langle z,w\rangle =z_{1}{\overline {w}}_{1}+z_{2}{\overline {w}}_{2}\,.} The real part of ⟨z,w⟩ is then the four-dimensional Euclidean dot product. <span>This inner product is Hermitian symmetric, which means that the result of interchanging z and w is the complex conjugate: ⟨ w , z ⟩ = ⟨ z , w







Flashcard 1759711989004

Tags
#calculus
Question
an infinite series of numbers is said to converge absolutely if [...]
Answer
the sum of the absolute values of the summands is finite.


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In mathematics, an infinite series of numbers is said to converge absolutely if the sum of the absolute values of the summands is finite.

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Absolute convergence - Wikipedia
of references, but its sources remain unclear because it has insufficient inline citations. Please help to improve this article by introducing more precise citations. (February 2013) (Learn how and when to remove this template message) <span>In mathematics, an infinite series of numbers is said to converge absolutely (or to be absolutely convergent) if the sum of the absolute values of the summands is finite. More precisely, a real or complex series ∑ n = 0







Flashcard 1759713561868

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#calculus
Question
an infinite series of numbers is said to [...] if the sum of the absolute values of the summands is finite.
Answer
converge absolutely


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In mathematics, an infinite series of numbers is said to converge absolutely if the sum of the absolute values of the summands is finite.

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Absolute convergence - Wikipedia
of references, but its sources remain unclear because it has insufficient inline citations. Please help to improve this article by introducing more precise citations. (February 2013) (Learn how and when to remove this template message) <span>In mathematics, an infinite series of numbers is said to converge absolutely (or to be absolutely convergent) if the sum of the absolute values of the summands is finite. More precisely, a real or complex series ∑ n = 0







Flashcard 1759715134732

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#hilbert-space
Question
Linear operators on a Hilbert space are simply transformations that [...]
Answer
stretch the space by different factors in mutually perpendicular directions


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Linear operators on a Hilbert space are likewise fairly concrete objects: in good cases, they are simply transformations that stretch the space by different factors in mutually perpendicular directions in a sense that is made precise by the study of their spectrum.

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Hilbert space - Wikipedia
is countably infinite, this means that the Hilbert space can also usefully be thought of in terms of the space of infinite sequences that are square-summable. The latter space is often in the older literature referred to as the Hilbert space. <span>Linear operators on a Hilbert space are likewise fairly concrete objects: in good cases, they are simply transformations that stretch the space by different factors in mutually perpendicular directions in a sense that is made precise by the study of their spectrum. Contents [hide] 1 Definition and illustration 1.1 Motivating example: Euclidean space 1.2 Definition 1.3 Second example: sequence spaces 2 History 3 Examples 3.1 Lebesgu







Flashcard 1759717494028

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#hilbert-space
Question
The effect of Linear operators on a Hilbert space can be understood by the study of [...].
Answer
their spectrum.


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Linear operators on a Hilbert space are likewise fairly concrete objects: in good cases, they are simply transformations that stretch the space by different factors in mutually perpendicular directions in a sense that is made precise by the study of their spectrum.

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Hilbert space - Wikipedia
is countably infinite, this means that the Hilbert space can also usefully be thought of in terms of the space of infinite sequences that are square-summable. The latter space is often in the older literature referred to as the Hilbert space. <span>Linear operators on a Hilbert space are likewise fairly concrete objects: in good cases, they are simply transformations that stretch the space by different factors in mutually perpendicular directions in a sense that is made precise by the study of their spectrum. Contents [hide] 1 Definition and illustration 1.1 Motivating example: Euclidean space 1.2 Definition 1.3 Second example: sequence spaces 2 History 3 Examples 3.1 Lebesgu







Flashcard 1759720639756

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#hilbert-space
Question
When that set of axes is countably infinite, the Hilbert space can also be usefully thought of in terms of the space of [...]


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When that set of axes is countably infinite, the Hilbert space can also be usefully thought of in terms of the space of infinite sequences that are square-summable.

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Hilbert space - Wikipedia
mization problems and other aspects of the theory. An element of a Hilbert space can be uniquely specified by its coordinates with respect to a set of coordinate axes (an orthonormal basis), in analogy with Cartesian coordinates in the plane. <span>When that set of axes is countably infinite, the Hilbert space can also be usefully thought of in terms of the space of infinite sequences that are square-summable. The latter space is often in the older literature referred to as the Hilbert space. Linear operators on a Hilbert space are likewise fairly concrete objects: in good cases, they are sim







Flashcard 1759722999052

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#hilbert-space
Question
When [...], the Hilbert space can also be usefully thought of in terms of the space of infinite sequences that are square-summable.
Answer
that set of axes is countably infinite


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When that set of axes is countably infinite, the Hilbert space can also be usefully thought of in terms of the space of infinite sequences that are square-summable.

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Hilbert space - Wikipedia
mization problems and other aspects of the theory. An element of a Hilbert space can be uniquely specified by its coordinates with respect to a set of coordinate axes (an orthonormal basis), in analogy with Cartesian coordinates in the plane. <span>When that set of axes is countably infinite, the Hilbert space can also be usefully thought of in terms of the space of infinite sequences that are square-summable. The latter space is often in the older literature referred to as the Hilbert space. Linear operators on a Hilbert space are likewise fairly concrete objects: in good cases, they are sim







#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 <span>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




Flashcard 1759749475596

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#spanish
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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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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 <span>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







Flashcard 1759762844940

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#hilbert-space
Question
At a deeper level, [...] plays a significant role in optimization problems and other aspects of the theory.
Answer
perpendicular projection onto a subspace


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At a deeper level, perpendicular projection onto a subspace plays a significant role in optimization problems and other aspects of the theory.

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Hilbert space - Wikipedia
f generalized functions, and Hardy spaces of holomorphic functions. Geometric intuition plays an important role in many aspects of Hilbert space theory. Exact analogs of the Pythagorean theorem and parallelogram law hold in a Hilbert space. <span>At a deeper level, perpendicular projection onto a subspace (the analog of "dropping the altitude" of a triangle) plays a significant role in optimization problems and other aspects of the theory. An element of a Hilbert space can be uniquely specified by its coordinates with respect to a set of coordinate axes (an orthonormal basis), in analogy with Cartesian coordinates in the







Types of Properties to Buy . . . And Avoid

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consider going after the properties that are truly run down, both in appearance and structure. But even then, the easiest money to be made will be in the properties that look simply awful, but need only skin-deep renovations. You’ll be trying to find these deals your whole investing career.

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Cosmetic repairs include minor items such as interior carpets, ap- pliances, and paint. On the exterior, it may include light repairs on woodwork, roofing, and siding.

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On a typical cosmetic repositioning, expect to spend on interior and exterior repairs between $1,000 and $4,000 per unit. Above $4,000, it’s becoming a major repair job, and the risk is going up. The more repairs, the more unknowns you may uncover. That means you could end up spending more, taking longer, or both.

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Avoid any repair that does not increase the value of the property. Almost all cosmetic repairs increase the value of the property, but many expensive structural and environmental repairs do not.

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Don’t think you can just wait a while and pawn the property off on someone else. You are risking the loss of your certificate of occupancy.

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Black mold. Just because it’s black mold doesn’t mean it’s toxic. A mold specialist can determine what you’re dealing with. But the fact that it is mold is a problem. Even when not toxic, mold causes many health problems.

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Normally, a mold cleanup is not difficult. You must remove all the drywall and any other material covering the walls, down to the studs. The real problem lies in where the water source is that caused the mold.

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Sometimes, the water source cannot be isolated and repaired. For instance, a high water table is not economically fixable. If your prop- erty inspector found this situation, just pay his inspection bill and move on to the next property.

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High vacancies are one of the easiest problems to cure.

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et up a web page and direct people to it. Did you know that almost 30 percent of potential applicants come from the Web? Then we will do a postcard campaign to people living in build- ings like ours and tempt them to move to ours. They have already indicated that they like our building style; now it’s up to us to make it more enticing to live at our place than where they currently reside.

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contact the human resource managers at all major employers in the area. It’s in their best interest to find housing for their employees, so let’s make it easy for them to do just that.

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Remember, the slow payers, non-payers, and criminals go first.

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7.0.0 The ASP tags <%, %>, <%=, and the script tag

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