# on 13-May-2018 (Sun)

#### Flashcard 1731750923532

Question
[...] tends to indicate motion backward, while [...] tends to refer to place
Atrás, detrás

Tuvo que volver atrás.

Fumaba un cigarrillo detrás de otro.

status measured difficulty not learned 37% [default] 0
¿Detrás or Atrás — Which Spanish Adverb Should I Use?
Updated May 15, 2017 Although both detrás and atrás are adverbs that can be translated as "behind" and are often listed as synonyms, they tend to be used in different ways. <span>Atrás tends to indicate motion backward, while detrás tends to refer to place, but the distinction isn't always clear. Sometimes the choice of word is a matter of which "sounds better" rather than following some fixed rule. That said, it is probably eas

#### Annotation 1758256303372

#weak-formulation
Weak formulations are important tools for the analysis of mathematical equations that permit the transfer of concepts of linear algebra to solve problems in other fields such as partial differential equations. In a weak formulation, an equation is no longer required to hold absolutely (and this is not even well defined) and has instead weak solutions only with respect to certain "test vectors" or "test functions".

Weak formulation - Wikipedia
Weak formulation - Wikipedia Weak formulation From Wikipedia, the free encyclopedia Jump to: navigation, search Weak formulations are important tools for the analysis of mathematical equations that permit the transfer of concepts of linear algebra to solve problems in other fields such as partial differential equations. In a weak formulation, an equation is no longer required to hold absolutely (and this is not even well defined) and has instead weak solutions only with respect to certain "test vectors" or "test functions". This is equivalent to formulating the problem to require a solution in the sense of a distribution. [citation needed] We introduce weak formulations by a few examples and present the

#### Annotation 1758258662668

#weak-formulation
Weak formulations transfer concepts of linear algebra to solve problems in other fields such as partial differential equations.

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Weak formulations are important tools for the analysis of mathematical equations that permit the transfer of concepts of linear algebra to solve problems in other fields such as partial differential equations. In a weak formulation, an equation is no longer required to hold absolutely (and this is not even well defined) and has instead weak solutions only with respect to certain "test ve

#### Original toplevel document

Weak formulation - Wikipedia
Weak formulation - Wikipedia Weak formulation From Wikipedia, the free encyclopedia Jump to: navigation, search Weak formulations are important tools for the analysis of mathematical equations that permit the transfer of concepts of linear algebra to solve problems in other fields such as partial differential equations. In a weak formulation, an equation is no longer required to hold absolutely (and this is not even well defined) and has instead weak solutions only with respect to certain "test vectors" or "test functions". This is equivalent to formulating the problem to require a solution in the sense of a distribution. [citation needed] We introduce weak formulations by a few examples and present the

#### Flashcard 1758265478412

Tags
#weak-formulation
Question
[...] transfer concepts of linear algebra to solve problems in other fields such as partial differential equations.
Weak formulations

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Weak formulations transfer concepts of linear algebra to solve problems in other fields such as partial differential equations.

#### Original toplevel document

Weak formulation - Wikipedia
Weak formulation - Wikipedia Weak formulation From Wikipedia, the free encyclopedia Jump to: navigation, search Weak formulations are important tools for the analysis of mathematical equations that permit the transfer of concepts of linear algebra to solve problems in other fields such as partial differential equations. In a weak formulation, an equation is no longer required to hold absolutely (and this is not even well defined) and has instead weak solutions only with respect to certain "test vectors" or "test functions". This is equivalent to formulating the problem to require a solution in the sense of a distribution. [citation needed] We introduce weak formulations by a few examples and present the

#### Flashcard 2965663780108

Tags
#viterbi-algorithm
Question
This algorithm generates a path [...], which is a sequence of states $${\displaystyle x_{n}\in S=\{s_{1},s_{2},\dots ,s_{K}\}}$$ that generate the observations $${\displaystyle Y=(y_{1},y_{2},\ldots ,y_{T})}$$ with $${\displaystyle y_{n}\in O=\{o_{1},o_{2},\dots ,o_{N}\}}$$ ($$N$$ being the count of observations (observation space, see below)).
$${\displaystyle X=(x_{1},x_{2},\ldots ,x_{T})}$$

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This algorithm generates a path $${\displaystyle X=(x_{1},x_{2},\ldots ,x_{T})}$$, which is a sequence of states $${\displaystyle x_{n}\in S=\{s_{1},s_{2},\dots ,s_{K}\}}$$ that generate the observations $${\displaystyle Y=(y_{1},y_{2},\ldots ,y_{T})}$$ with $${\disp #### Original toplevel document Viterbi algorithm - Wikipedia lly needs to, and usually manages to get away with doing a lot less work (in software) than the ordinary Viterbi algorithm for the same result—however, it is not so easy [clarification needed] to parallelize in hardware. Pseudocode <span>This algorithm generates a path X = ( x 1 , x 2 , … , x T ) {\displaystyle X=(x_{1},x_{2},\ldots ,x_{T})} , which is a sequence of states x n ∈ S = { s 1 , s 2 , … , s K } {\displaystyle x_{n}\in S=\{s_{1},s_{2},\dots ,s_{K}\}} that generate the observations Y = ( y 1 , y 2 , … , y T ) {\displaystyle Y=(y_{1},y_{2},\ldots ,y_{T})} with y n ∈ O = { o 1 , o 2 , … , o N } {\displaystyle y_{n}\in O=\{o_{1},o_{2},\dots ,o_{N}\}} ( N {\displaystyle N} being the count of observations (observation space, see below)). Two 2-dimensional tables of size K × T {\displaystyle K\times T} are constructed: Each element #### Flashcard 2965691567372 Tags #weak-formulation Question Weak formulations transfer [...] to solve problems in other fields such as partial differential equations. Answer status measured difficulty not learned 37% [default] 0 #### Parent (intermediate) annotation Open it Weak formulations transfer concepts of linear algebra to solve problems in other fields such as partial differential equations. #### Original toplevel document Weak formulation - Wikipedia Weak formulation - Wikipedia Weak formulation From Wikipedia, the free encyclopedia Jump to: navigation, search Weak formulations are important tools for the analysis of mathematical equations that permit the transfer of concepts of linear algebra to solve problems in other fields such as partial differential equations. In a weak formulation, an equation is no longer required to hold absolutely (and this is not even well defined) and has instead weak solutions only with respect to certain "test vectors" or "test functions". This is equivalent to formulating the problem to require a solution in the sense of a distribution. [citation needed] We introduce weak formulations by a few examples and present the #### Annotation 2965694450956 #linear-algebra The main structures of linear algebra are vector spaces. status not read Linear algebra - Wikipedia century applications, such as data mining and uncertainty analysis, linear algebra can be based upon the SVD instead of Gaussian Elimination. [13] [14] Scope of study[edit source] Vector spaces[edit source] Main article: Vector space <span>The main structures of linear algebra are vector spaces. A vector space over a field F (often the field of the real numbers) is a set V equipped with two binary operations satisfying the following axioms. Elements of V are called vectors, and #### Annotation 2965696548108 #linear-algebra Given two vector spaces V and W over a field F, a linear transformation (also called linear map, linear mapping or linear operator) is a map \(T:V\to W$$

that is compatible with addition and scalar multiplication:

$$T(u+v)=T(u)+T(v),\quad T(av)=aT(v)$$

for any vectors u,vV and a scalar aF.

Linear algebra - Wikipedia
to all vector spaces. Linear transformations[edit source] Main article: Linear map Similarly as in the theory of other algebraic structures, linear algebra studies mappings between vector spaces that preserve the vector-space structure. <span>Given two vector spaces V and W over a field F, a linear transformation (also called linear map, linear mapping or linear operator) is a map T : V → W {\displaystyle T:V\to W} that is compatible with addition and scalar multiplication: T ( u + v ) = T ( u ) + T ( v ) , T ( a v ) = a T ( v ) {\displaystyle T(u+v)=T(u)+T(v),\quad T(av)=aT(v)} for any vectors u,v ∈ V and a scalar a ∈ F. Additionally for any vectors u, v ∈ V and scalars a, b ∈ F: T ( a u + b v ) =

#### Annotation 2965703888140

[unknown IMAGE 2965705723148]
#has-images #mapping
an injective function never maps distinct elements of its domain to the same element of its codomain.

Injective function - Wikipedia
raic · Analytic · Smooth · Continuous · Measurable · Injective · Surjective · Bijective   Constructions   Restriction · Composition · λ · Inverse   Generalizations   Partial · Multivalued · Implicit v t e In mathematics, <span>an injective function or injection or one-to-one function is a function that preserves distinctness: it never maps distinct elements of its domain to the same element of its codomain. In other words, every element of the function's codomain is the image of at most one element of its domain. The term one-to-one function must not be confused with one-to-one corresponde

#### Flashcard 2965707820300

[unknown IMAGE 2965705723148]
Tags
#has-images #mapping
Question
an injective function never [maps...to...]
maps distinct elements of its domain to the same element of its codomain.

status measured difficulty not learned 37% [default] 0

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an injective function never maps distinct elements of its domain to the same element of its codomain.

#### Original toplevel document

Injective function - Wikipedia
raic · Analytic · Smooth · Continuous · Measurable · Injective · Surjective · Bijective   Constructions   Restriction · Composition · λ · Inverse   Generalizations   Partial · Multivalued · Implicit v t e In mathematics, <span>an injective function or injection or one-to-one function is a function that preserves distinctness: it never maps distinct elements of its domain to the same element of its codomain. In other words, every element of the function's codomain is the image of at most one element of its domain. The term one-to-one function must not be confused with one-to-one corresponde

#### Flashcard 2965710179596

[unknown IMAGE 2965705723148]
Tags
#has-images #mapping
Question
an [...] function never maps distinct elements of its domain to the same element of its codomain.
injective

Also called one-to-one function

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an injective function never maps distinct elements of its domain to the same element of its codomain.

#### Original toplevel document

Injective function - Wikipedia
raic · Analytic · Smooth · Continuous · Measurable · Injective · Surjective · Bijective   Constructions   Restriction · Composition · λ · Inverse   Generalizations   Partial · Multivalued · Implicit v t e In mathematics, <span>an injective function or injection or one-to-one function is a function that preserves distinctness: it never maps distinct elements of its domain to the same element of its codomain. In other words, every element of the function's codomain is the image of at most one element of its domain. The term one-to-one function must not be confused with one-to-one corresponde

#### Annotation 2965717781772

[unknown IMAGE 2965720403212]
#has-images #mapping
With a surjective (or onto) function f, for every element in the codomain Y there is at least one element x in the domain X such that f(x) = y.

Surjective function - Wikipedia
raic · Analytic · Smooth · Continuous · Measurable · Injective · Surjective · Bijective   Constructions   Restriction · Composition · λ · Inverse   Generalizations   Partial · Multivalued · Implicit v t e In mathematics, <span>a function f from a set X to a set Y is surjective (or onto), or a surjection, if for every element y in the codomain Y of f there is at least one element x in the domain X of f such that f(x) = y. It is not required that x is unique; the function f may map one or more elements of X to the same element of Y. [imagelink] A surjective function from domain X to codomain Y. T

#### Flashcard 2965722500364

[unknown IMAGE 2965720403212]
Tags
#has-images #mapping
Question
a surjective (or onto) function f satisfies that [...].
for every element in the codomain Y there is at least one element x in the domain X such that f(x) = y

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With a surjective (or onto) function f, for every element in the codomain Y there is at least one element x in the domain X such that f(x) = y.

#### Original toplevel document

Surjective function - Wikipedia
raic · Analytic · Smooth · Continuous · Measurable · Injective · Surjective · Bijective   Constructions   Restriction · Composition · λ · Inverse   Generalizations   Partial · Multivalued · Implicit v t e In mathematics, <span>a function f from a set X to a set Y is surjective (or onto), or a surjection, if for every element y in the codomain Y of f there is at least one element x in the domain X of f such that f(x) = y. It is not required that x is unique; the function f may map one or more elements of X to the same element of Y. [imagelink] A surjective function from domain X to codomain Y. T

#### Flashcard 2965724859660

[unknown IMAGE 2965720403212]
Tags
#has-images #mapping
Question
a [...] function f satisfies that, for every element in the codomain Y there is at least one element x in the domain X such that f(x) = y
surjective

(or onto) function

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With a surjective (or onto) function f, for every element in the codomain Y there is at least one element x in the domain X such that f(x) = y.

#### Original toplevel document

Surjective function - Wikipedia
raic · Analytic · Smooth · Continuous · Measurable · Injective · Surjective · Bijective   Constructions   Restriction · Composition · λ · Inverse   Generalizations   Partial · Multivalued · Implicit v t e In mathematics, <span>a function f from a set X to a set Y is surjective (or onto), or a surjection, if for every element y in the codomain Y of f there is at least one element x in the domain X of f such that f(x) = y. It is not required that x is unique; the function f may map one or more elements of X to the same element of Y. [imagelink] A surjective function from domain X to codomain Y. T

#### Annotation 2965727481100

[unknown IMAGE 2965735083276]
#has-images #mapping
a bijective function a one-to-one and onto (surjective) mapping of a set X to a set Y.

Bijection - Wikipedia
nction between the elements of two sets, where each element of one set is paired with exactly one element of the other set, and each element of the other set is paired with exactly one element of the first set. There are no unpaired elements. <span>In mathematical terms, a bijective function f: X → Y is a one-to-one (injective) and onto (surjective) mapping of a set X to a set Y. A bijection from the set X to the set Y has an inverse function from Y to X. If X and Y are finite sets, then the existence of a bijection means they have the same number of elements.

#### Flashcard 2965737180428

[unknown IMAGE 2965735083276]
Tags
#has-images #mapping
Question
a bijective function is a [...] mapping of a set X to a set Y.

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a bijective function a one-to-one and onto (surjective) mapping of a set X to a set Y.

#### Original toplevel document

Bijection - Wikipedia
nction between the elements of two sets, where each element of one set is paired with exactly one element of the other set, and each element of the other set is paired with exactly one element of the first set. There are no unpaired elements. <span>In mathematical terms, a bijective function f: X → Y is a one-to-one (injective) and onto (surjective) mapping of a set X to a set Y. A bijection from the set X to the set Y has an inverse function from Y to X. If X and Y are finite sets, then the existence of a bijection means they have the same number of elements.

#### Flashcard 2965739539724

[unknown IMAGE 2965735083276]
Tags
#has-images #mapping
Question
a [...] function is a one-to-one and onto mapping of a set X to a set Y.
bijective

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a bijective function a one-to-one and onto (surjective) mapping of a set X to a set Y.

#### Original toplevel document

Bijection - Wikipedia
nction between the elements of two sets, where each element of one set is paired with exactly one element of the other set, and each element of the other set is paired with exactly one element of the first set. There are no unpaired elements. <span>In mathematical terms, a bijective function f: X → Y is a one-to-one (injective) and onto (surjective) mapping of a set X to a set Y. A bijection from the set X to the set Y has an inverse function from Y to X. If X and Y are finite sets, then the existence of a bijection means they have the same number of elements.

#### Annotation 2965742161164

#linear-algebra
When a bijective linear mapping exists between two vector spaces (that is, every vector from the second space is associated with exactly one in the first), we say that the two spaces are isomorphic.

Linear algebra - Wikipedia
T ( b v ) = a T ( u ) + b T ( v ) {\displaystyle \quad T(au+bv)=T(au)+T(bv)=aT(u)+bT(v)} <span>When a bijective linear mapping exists between two vector spaces (that is, every vector from the second space is associated with exactly one in the first), we say that the two spaces are isomorphic. Because an isomorphism preserves linear structure, two isomorphic vector spaces are "essentially the same" from the linear algebra point of view. One essential question in lin

#### Annotation 2965746879756

#mapping

the kernel (also known as null space or nullspace) of a linear map L : VW between two vector spaces V and W, is the set of all elements v of V that are mapped to the zero vector in W.

$${\displaystyle \ker(L)=\left\{\mathbf {v} \in V\mid L(\mathbf {v} )=\mathbf {0} \right\}{\text{.}}}$$

Kernel (linear algebra) - Wikipedia
From Wikipedia, the free encyclopedia (Redirected from Kernel (linear operator)) Jump to: navigation, search In mathematics, and more specifically in linear algebra and functional analysis, <span>the kernel (also known as null space or nullspace) of a linear map L : V → W between two vector spaces V and W, is the set of all elements v of V for which L(v) = 0, where 0 denotes the zero vector in W. That is, in set-builder notation, ker ⁡ ( L ) = { v ∈ V ∣ L ( v ) = 0 } . {\displaystyle \ker(L)=\left\{\mathbf {v} \in V\mid L(\mathbf {v} )=\mathbf {0} \right\}{\text{.}}} Contents [hide] 1 Properties 2 Application to modules 3 In functional analysis 4 Representation as matrix multiplication 4.1 Subspace properties 4.2 The row space of a

#### Annotation 2965748452620

#linear-algebra

Linear transformations have geometric significance. For example, 2 × 2 real matrices denote standard planar mappings that preserve the origin.

Linear algebra - Wikipedia
n can be answered by checking if the determinant is nonzero. If a mapping is not an isomorphism, linear algebra is interested in finding its range (or image) and the set of elements that get mapped to zero, called the kernel of the mapping. <span>Linear transformations have geometric significance. For example, 2 × 2 real matrices denote standard planar mappings that preserve the origin. Subspaces, span, and basis[edit source] Main articles: Linear subspace, Linear span, and Basis (linear algebra) Again, in analogue with theories of other algebraic objects, linear

#### Flashcard 2965751336204

Tags
#mapping
Question

the kernel of a linear map L : VW between two vector spaces V and W, is the set of all elements v of V that [...]

are mapped to the zero vector in W

status measured difficulty not learned 37% [default] 0

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the kernel (also known as null space or nullspace) of a linear map L : V → W between two vector spaces V and W, is the set of all elements v of V that are mapped to the zero vector in W. $${\displaystyle \ker(L)=\left\{\mathbf {v} \in V\mid L(\mathbf {v} )=\mathbf {0} \right\}{\text{.}}}$$

#### Original toplevel document

Kernel (linear algebra) - Wikipedia
From Wikipedia, the free encyclopedia (Redirected from Kernel (linear operator)) Jump to: navigation, search In mathematics, and more specifically in linear algebra and functional analysis, <span>the kernel (also known as null space or nullspace) of a linear map L : V → W between two vector spaces V and W, is the set of all elements v of V for which L(v) = 0, where 0 denotes the zero vector in W. That is, in set-builder notation, ker ⁡ ( L ) = { v ∈ V ∣ L ( v ) = 0 } . {\displaystyle \ker(L)=\left\{\mathbf {v} \in V\mid L(\mathbf {v} )=\mathbf {0} \right\}{\text{.}}} Contents [hide] 1 Properties 2 Application to modules 3 In functional analysis 4 Representation as matrix multiplication 4.1 Subspace properties 4.2 The row space of a

#### Flashcard 2965753695500

Tags
#mapping
Question

the kernel of a linear map L : VW between two vector spaces V and W, is the set [...math representation...]

$${\displaystyle \ker(L)=\left\{\mathbf {v} \in V\mid L(\mathbf {v} )=\mathbf {0} \right\}{\text{.}}}$$

status measured difficulty not learned 37% [default] 0

#### Parent (intermediate) annotation

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the kernel (also known as null space or nullspace) of a linear map L : V → W between two vector spaces V and W, is the set of all elements v of V that are mapped to the zero vector in W. $${\displaystyle \ker(L)=\left\{\mathbf {v} \in V\mid L(\mathbf {v} )=\mathbf {0} \right\}{\text{.}}}$$

#### Original toplevel document

Kernel (linear algebra) - Wikipedia
From Wikipedia, the free encyclopedia (Redirected from Kernel (linear operator)) Jump to: navigation, search In mathematics, and more specifically in linear algebra and functional analysis, <span>the kernel (also known as null space or nullspace) of a linear map L : V → W between two vector spaces V and W, is the set of all elements v of V for which L(v) = 0, where 0 denotes the zero vector in W. That is, in set-builder notation, ker ⁡ ( L ) = { v ∈ V ∣ L ( v ) = 0 } . {\displaystyle \ker(L)=\left\{\mathbf {v} \in V\mid L(\mathbf {v} )=\mathbf {0} \right\}{\text{.}}} Contents [hide] 1 Properties 2 Application to modules 3 In functional analysis 4 Representation as matrix multiplication 4.1 Subspace properties 4.2 The row space of a

#### Flashcard 2965756054796

Tags
#mapping
Question

the kernel is also known as [...]

null space

status measured difficulty not learned 37% [default] 0

Open it
the kernel (also known as null space or nullspace) of a linear map L : V → W between two vector spaces V and W, is the set of all elements v of V that are mapped to the zero vector in W. $${\displaystyle \ker(L)=\le #### Original toplevel document Kernel (linear algebra) - Wikipedia From Wikipedia, the free encyclopedia (Redirected from Kernel (linear operator)) Jump to: navigation, search In mathematics, and more specifically in linear algebra and functional analysis, <span>the kernel (also known as null space or nullspace) of a linear map L : V → W between two vector spaces V and W, is the set of all elements v of V for which L(v) = 0, where 0 denotes the zero vector in W. That is, in set-builder notation, ker ⁡ ( L ) = { v ∈ V ∣ L ( v ) = 0 } . {\displaystyle \ker(L)=\left\{\mathbf {v} \in V\mid L(\mathbf {v} )=\mathbf {0} \right\}{\text{.}}} Contents [hide] 1 Properties 2 Application to modules 3 In functional analysis 4 Representation as matrix multiplication 4.1 Subspace properties 4.2 The row space of a #### Annotation 2965758414092 #linear-algebra If a mapping is not an isomorphism, linear algebra is interested in finding its range (or image) and the set of elements that get mapped to zero, called the kernel of the mapping. status not read Linear algebra - Wikipedia s are "essentially the same" from the linear algebra point of view. One essential question in linear algebra is whether a mapping is an isomorphism or not, and this question can be answered by checking if the determinant is nonzero. <span>If a mapping is not an isomorphism, linear algebra is interested in finding its range (or image) and the set of elements that get mapped to zero, called the kernel of the mapping. Linear transformations have geometric significance. For example, 2 × 2 real matrices denote standard planar mappings that preserve the origin. Subspaces, span, and basis[edit source #### Flashcard 2965760511244 Tags #linear-algebra Question geometrically 2 × 2 real matrices denote [...]. Answer standard origin preserving planar mappings status measured difficulty not learned 37% [default] 0 #### Parent (intermediate) annotation Open it Linear transformations have geometric significance. For example, 2 × 2 real matrices denote standard planar mappings that preserve the origin. #### Original toplevel document Linear algebra - Wikipedia n can be answered by checking if the determinant is nonzero. If a mapping is not an isomorphism, linear algebra is interested in finding its range (or image) and the set of elements that get mapped to zero, called the kernel of the mapping. <span>Linear transformations have geometric significance. For example, 2 × 2 real matrices denote standard planar mappings that preserve the origin. Subspaces, span, and basis[edit source] Main articles: Linear subspace, Linear span, and Basis (linear algebra) Again, in analogue with theories of other algebraic objects, linear #### Flashcard 2965763656972 Tags #linear-algebra Question two spaces are [...] if a bijective linear mapping exists between them Answer isomorphic status measured difficulty not learned 37% [default] 0 #### Parent (intermediate) annotation Open it When a bijective linear mapping exists between two vector spaces (that is, every vector from the second space is associated with exactly one in the first), we say that the two spaces are isomorphic. #### Original toplevel document Linear algebra - Wikipedia T ( b v ) = a T ( u ) + b T ( v ) {\displaystyle \quad T(au+bv)=T(au)+T(bv)=aT(u)+bT(v)} <span>When a bijective linear mapping exists between two vector spaces (that is, every vector from the second space is associated with exactly one in the first), we say that the two spaces are isomorphic. Because an isomorphism preserves linear structure, two isomorphic vector spaces are "essentially the same" from the linear algebra point of view. One essential question in lin #### Flashcard 2965766802700 Tags #linear-algebra Question Given two vector spaces V and W over a field F, a linear transformation \(T:V\to W$$

satisfies [...math representation...] for any vectors u,vV and a scalar aF.

$$T(u+v)=T(u)+T(v),\quad T(av)=aT(v)$$

operation preserving

status measured difficulty not learned 37% [default] 0

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><head>Given two vector spaces V and W over a field F, a linear transformation (also called linear map, linear mapping or linear operator) is a map $$T:V\to W$$ that is compatible with addition and scalar multiplication: $$T(u+v)=T(u)+T(v),\quad T(av)=aT(v)$$ for any vectors u,v ∈ V and a scalar a ∈ F. <html>

#### Original toplevel document

Linear algebra - Wikipedia
to all vector spaces. Linear transformations[edit source] Main article: Linear map Similarly as in the theory of other algebraic structures, linear algebra studies mappings between vector spaces that preserve the vector-space structure. <span>Given two vector spaces V and W over a field F, a linear transformation (also called linear map, linear mapping or linear operator) is a map T : V → W {\displaystyle T:V\to W} that is compatible with addition and scalar multiplication: T ( u + v ) = T ( u ) + T ( v ) , T ( a v ) = a T ( v ) {\displaystyle T(u+v)=T(u)+T(v),\quad T(av)=aT(v)} for any vectors u,v ∈ V and a scalar a ∈ F. Additionally for any vectors u, v ∈ V and scalars a, b ∈ F: T ( a u + b v ) =

#### Flashcard 2965769161996

Tags
#linear-algebra
Question
The main structures of linear algebra are [...].
vector spaces

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The main structures of linear algebra are vector spaces.

#### Original toplevel document

Linear algebra - Wikipedia
century applications, such as data mining and uncertainty analysis, linear algebra can be based upon the SVD instead of Gaussian Elimination. [13] [14] Scope of study[edit source] Vector spaces[edit source] Main article: Vector space <span>The main structures of linear algebra are vector spaces. A vector space over a field F (often the field of the real numbers) is a set V equipped with two binary operations satisfying the following axioms. Elements of V are called vectors, and

#### Flashcard 2965774929164

Tags
#linear-algebra
Question
If a mapping is not an isomorphism, linear algebra is interested in finding its [...and...]

status measured difficulty not learned 37% [default] 0

#### Parent (intermediate) annotation

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If a mapping is not an isomorphism, linear algebra is interested in finding its range (or image) and the set of elements that get mapped to zero, called the kernel of the mapping.

#### Original toplevel document

Linear algebra - Wikipedia
s are "essentially the same" from the linear algebra point of view. One essential question in linear algebra is whether a mapping is an isomorphism or not, and this question can be answered by checking if the determinant is nonzero. <span>If a mapping is not an isomorphism, linear algebra is interested in finding its range (or image) and the set of elements that get mapped to zero, called the kernel of the mapping. Linear transformations have geometric significance. For example, 2 × 2 real matrices denote standard planar mappings that preserve the origin. Subspaces, span, and basis[edit source

#### Annotation 2965843610892

#git-flow
git-flow are a set of git extensions to provide high-level repository operations for Vincent Driessen's branching model.

git-flow cheatsheet
) - Українська (Ukrainian) - Tiếng Việt (Vietnamese) - Polski - العربية - Lietuviškai (Lithuanian) - Azərbaycanca (Azerbaijani) Bahasa Indonesia About <span>git-flow are a set of git extensions to provide high-level repository operations for Vincent Driessen's branching model. more ★ ★ ★ This cheatsheet shows the basic usage and effect of git-flow operations ★ ★ ★ Basic tips Git flow provides excellent comma

#### Flashcard 2965845183756

Tags
#git-flow
Question
git-flow are a set of git extensions to provide [...] for Vincent Driessen's branching model.
high-level repository operations

status measured difficulty not learned 37% [default] 0

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git-flow are a set of git extensions to provide high-level repository operations for Vincent Driessen's branching model.

#### Original toplevel document

git-flow cheatsheet
) - Українська (Ukrainian) - Tiếng Việt (Vietnamese) - Polski - العربية - Lietuviškai (Lithuanian) - Azərbaycanca (Azerbaijani) Bahasa Indonesia About <span>git-flow are a set of git extensions to provide high-level repository operations for Vincent Driessen's branching model. more ★ ★ ★ This cheatsheet shows the basic usage and effect of git-flow operations ★ ★ ★ Basic tips Git flow provides excellent comma

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git-flow are a set of git extensions to provide high-level repository operations for Vincent Driessen's [...].
branching model

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git-flow are a set of git extensions to provide high-level repository operations for Vincent Driessen's branching model.

#### Original toplevel document

git-flow cheatsheet
) - Українська (Ukrainian) - Tiếng Việt (Vietnamese) - Polski - العربية - Lietuviškai (Lithuanian) - Azərbaycanca (Azerbaijani) Bahasa Indonesia About <span>git-flow are a set of git extensions to provide high-level repository operations for Vincent Driessen's branching model. more ★ ★ ★ This cheatsheet shows the basic usage and effect of git-flow operations ★ ★ ★ Basic tips Git flow provides excellent comma

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The repository setup that we use and that works well with this branching model, is that with a central “truth” repo.

A successful Git branching model » nvie.com
e development model. The model that I’m going to present here is essentially no more than a set of procedures that every team member has to follow in order to come to a managed software development process. Decentralized but centralized ¶ <span>The repository setup that we use and that works well with this branching model, is that with a central “truth” repo. Note that this repo is only considered to be the central one (since Git is a DVCS, there is no such thing as a central repo at a technical level). We will refer to this repo as origin

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The repository setup that we use and that works well with this branching model, is that with a [...].
central “truth” repo

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The repository setup that we use and that works well with this branching model, is that with a central “truth” repo.

#### Original toplevel document

A successful Git branching model » nvie.com
e development model. The model that I’m going to present here is essentially no more than a set of procedures that every team member has to follow in order to come to a managed software development process. Decentralized but centralized ¶ <span>The repository setup that we use and that works well with this branching model, is that with a central “truth” repo. Note that this repo is only considered to be the central one (since Git is a DVCS, there is no such thing as a central repo at a technical level). We will refer to this repo as origin

#### Annotation 2965855931660

#git-flow
The develop branch the default branch where most of the work will happen, and the master branch keeps track of production-ready code.

Using git-flow to automate your git branching workflow

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the [...] branch keeps track of production-ready code.
master

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The develop branch the default branch where most of the work will happen, and the master branch keeps track of production-ready code.

#### Original toplevel document

Using git-flow to automate your git branching workflow
hing to change or remove, you just stop using the git-flow commands. If you run git branch after setting up, you’ll notice that you switched from the master branch to a new one named develop . \$ git branch * develop master <span>The develop branch the default branch where most of the work will happen, and the master branch keeps track of production-ready code. Feature branches git-flow makes it easy to work on multiple features at the same time by using feature branches. To start one, use feature start with the name of your

#### Annotation 2965866941708

#git #git-config
Configuration Files
##### Repository specific configuration file [--local]:
<repo>/.git/config

##### User-specific configuration file [--global]:
~/.gitconfig

##### System-wide configuration file [--system]:
/etc/gitconfig


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##### Repository specific configuration file [--local]: [...]

<repo>/.git/config

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#### Original toplevel document

GitHub - arslanbilal/git-cheat-sheet: git and git flow cheat sheet

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##### User-specific configuration file [--global]: [...]

~/.gitconfig

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Configuration Files Repository specific configuration file [--local]: /.git/config User-specific configuration file [--global]: ~/.gitconfig System-wide configuration file [--system]: /etc/gitconfig

#### Original toplevel document

GitHub - arslanbilal/git-cheat-sheet: git and git flow cheat sheet

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#git #git-config
##### System-wide configuration file [--system]:
/etc/gitconfig


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ad><head>Configuration Files Repository specific configuration file [--local]: /.git/config User-specific configuration file [--global]: ~/.gitconfig System-wide configuration file [--system]: /etc/gitconfig <html>

#### Original toplevel document

GitHub - arslanbilal/git-cheat-sheet: git and git flow cheat sheet

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##### System-wide configuration file [--system]: [...]
/etc/gitconfig


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System-wide configuration file [--system]: /etc/gitconfig

#### Original toplevel document

GitHub - arslanbilal/git-cheat-sheet: git and git flow cheat sheet

#### Annotation 2965881883916

#best-practice #git
Commit should be done Early And Often

Commit Often, Perfect Later, Publish Once—Git Best Practices
e something. People resist this out of some sense that this is ugly, limits git-bisect ion functionality, is confusing to observers, and might lead to accusations of stupidity. Well, I’m here to tell you that resisting this is ignorant. <span>Commit Early And Often. If, after you are done, you want to pretend to the outside world that your work sprung complete from your mind into the repository in utter perfection with each concept fully thought

#### Annotation 2965883456780

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You should commit or stash your current work before performing any recovery efforts

Commit Often, Perfect Later, Publish Once—Git Best Practices
fixing, or removing commits in git if you want to fix a particular problematic commit or commits, as opposed to attempting to locate lost data. When attempting to find your lost commits, first make sure you will not lose any current work. <span>You should commit or stash your current work before performing any recovery efforts that might destroy your current work and perhaps take backups of it (see Backups below). After finding the commits you can reset , rebase , cherry-pick , merge , or otherwise do wha

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You should [...] before performing any recovery efforts
commit or stash your current work

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You should commit or stash your current work before performing any recovery efforts

#### Original toplevel document

Commit Often, Perfect Later, Publish Once—Git Best Practices
fixing, or removing commits in git if you want to fix a particular problematic commit or commits, as opposed to attempting to locate lost data. When attempting to find your lost commits, first make sure you will not lose any current work. <span>You should commit or stash your current work before performing any recovery efforts that might destroy your current work and perhaps take backups of it (see Backups below). After finding the commits you can reset , rebase , cherry-pick , merge , or otherwise do wha

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Commit should be done [...]
Early And Often

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Commit should be done Early And Often

#### Original toplevel document

Commit Often, Perfect Later, Publish Once—Git Best Practices
e something. People resist this out of some sense that this is ugly, limits git-bisect ion functionality, is confusing to observers, and might lead to accusations of stupidity. Well, I’m here to tell you that resisting this is ignorant. <span>Commit Early And Often. If, after you are done, you want to pretend to the outside world that your work sprung complete from your mind into the repository in utter perfection with each concept fully thought

#### Flashcard 2965888961804

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don't commit anything that can be [...] .

regenerated from other committed files

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Commit Often, Perfect Later, Publish Once—Git Best Practices
that there are legitimate reasons to do all of these. However, you should not attempt any of these things without understanding the potential negative effects of each and why they might be in a best practices “Don’t” list. DO NOT <span>commit anything that can be regenerated from other things that were committed. Things that can be regenerated include binaries, object files, jars, .class , flex/yacc generated code, etc. Really the only place there is room for disagreement about this

#### Flashcard 2965891321100

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don't commit [...] , especially those that might change from environment to environment or for any reasons.

configuration files

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Commit Often, Perfect Later, Publish Once—Git Best Practices
might take hours to regenerate (rendered images, e.g., but see Dividing work into repositories for more best practices about this) or autoconf generated files (so people can configure and compile without autotools installed). <span>commit configuration files Specifically configuration files that might change from environment to environment or for any reasons. See Information about local versions of configuration files use git as a web deployment tool Yes it can be done in a sufficiently simple/non-critical environment

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don't commit [...] , not everyone is using the same memory configuration you are.

large binary files

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Commit Often, Perfect Later, Publish Once—Git Best Practices
s document on using git to manage a web site to help, though there are other examples. However, this does not give you atomic updates, synchronized db updates, or other accouterments of an industrial deployment system. <span>commit large binary files (when possible) Large is currently relative to the amount of free RAM you have. Remember that not everyone may be using the same memory configuration you are. Support for large files is an active git topic, so watch for changes. After running a git gc you should be able to find the largest objects by running: git verify-p

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One commit should be a wrapper for [...] .