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Что (кто) такое linear algebra - определение

BRANCH OF MATHEMATICS THAT STUDIES VECTOR SPACES AND LINEAR TRANSFORMATIONS

LinearAlgebra; Linear alegebra; List of linear algebra references; Linear Algebra; Double eigenvalue; Linear Algebar; Applications of linear algebra; History of linear algebra

Найдено результатов: 1368

Numerical linear algebra

SUBFIELD OF NUMERICAL ANALYSIS AND A TYPE OF LINEAR ALGEBRA

Computational matrix algebra; Linear solver; Matrix computation; Applied linear algebra

Numerical linear algebra, sometimes called applied linear algebra, is the study of how matrix operations can be used to create computer algorithms which efficiently and accurately provide approximate answers to questions in continuous mathematics. It is a subfield of numerical analysis, and a type of linear algebra.

https://en.wikipedia.org/wiki/Numerical_linear_algebra

Linear Algebra and Its Applications

MATHEMATICAL JOURNAL

Linear Algebra Appl; Linear Algebra Appl.; Linear Algebra and its Applications; Linear Algebra Its Appl; Linear Algebra Its Appl.; Linear Algebra & Its Applications; Linear Algebra & its Applications

Linear Algebra and its Applications is a biweekly peer-reviewed mathematics journal published by Elsevier and covering matrix theory and finite-dimensional linear algebra.

https://en.wikipedia.org/wiki/Linear_Algebra_and_Its_Applications

Special linear Lie algebra

LIE ALGEBRA OF TRACELESS LINEAR TRANSFORMATIONS; LIE ALGEBRA OF THE SPECIAL LINEAR GROUP

Special linear algebra; Special linear lie algebra; Sl 2; Representation theory of sl 2; Draft:Special linear Lie algebra

In mathematics, the special linear Lie algebra of order n (denoted \mathfrak{sl}_n(F) or \mathfrak{sl}(n, F)) is the Lie algebra of n \times n matrices with trace zero and with the Lie bracket [X,Y]:=XY-YX. This algebra is well studied and understood, and is often used as a model for the study of other Lie algebras.

https://en.wikipedia.org/wiki/Special_linear_Lie_algebra

Outline of linear algebra

WIKIMEDIA LIST ARTICLE

Topics in linear algebra; Linear algebra topics; List of linear algebra topics

This is an outline of topics related to linear algebra, the branch of mathematics concerning linear equations and linear maps and their representations in vector spaces and through matrices.

https://en.wikipedia.org/wiki/Outline_of_linear_algebra

Nonlinear algebra

Draft:Nonlinear algebra

Nonlinear algebra is the nonlinear analogue to linear algebra, generalizing notions of spaces and transformations coming from the linear setting. Algebraic geometry is one of the main areas of mathematical research supporting nonlinear algebra, while major components coming from computational mathematics support the development of the area into maturity.

https://en.wikipedia.org/wiki/Nonlinear_algebra

linear map

$The function f:\R^2 \to \R^2 with f(x, y) = (2x, y) is a linear map. This function scales the x component of a vector by the factor 2.$
$The function f(x, y) = (2x, y) is additive: It doesn't matter whether vectors are first added and then mapped or whether they are mapped and finally added: f(\mathbf a + \mathbf b) = f(\mathbf a) + f(\mathbf b)$
$The function f(x, y) = (2x, y) is homogeneous: It doesn't matter whether a vector is first scaled and then mapped or first mapped and then scaled: f(\lambda \mathbf a) = \lambda f(\mathbf a)$

MAPPING THAT PRESERVES THE OPERATIONS OF ADDITION AND SCALAR MULTIPLICATION

Linear operator; Linear mapping; Linear transformations; Linear operators; Linear transform; Linear maps; Linear isomorphism; Linear isomorphic; Linear Transformation; Linear Transformations; Linear Operator; Homogeneous linear transformation; User:The Uber Ninja/X3; Linear transformation; Bijective linear map; Nonlinear operator; Linear Schrödinger Operator; Vector space homomorphism; Vector space isomorphism; Linear extension of a function; Linear extension (linear algebra); Extend by linearity; Linear endomorphism

<mathematics> (Or "linear transformation") A function from a vector space to a vector space which respects the additive and multiplicative structures of the two: that is, for any two vectors, u, v, in the source vector space and any scalar, k, in the field over which it is a vector space, a linear map f satisfies f(u+kv) = f(u) + kf(v). (1996-09-30)

Linear map

$The function f:\R^2 \to \R^2 with f(x, y) = (2x, y) is a linear map. This function scales the x component of a vector by the factor 2.$
$The function f(x, y) = (2x, y) is additive: It doesn't matter whether vectors are first added and then mapped or whether they are mapped and finally added: f(\mathbf a + \mathbf b) = f(\mathbf a) + f(\mathbf b)$
$The function f(x, y) = (2x, y) is homogeneous: It doesn't matter whether a vector is first scaled and then mapped or first mapped and then scaled: f(\lambda \mathbf a) = \lambda f(\mathbf a)$

MAPPING THAT PRESERVES THE OPERATIONS OF ADDITION AND SCALAR MULTIPLICATION

Linear operator; Linear mapping; Linear transformations; Linear operators; Linear transform; Linear maps; Linear isomorphism; Linear isomorphic; Linear Transformation; Linear Transformations; Linear Operator; Homogeneous linear transformation; User:The Uber Ninja/X3; Linear transformation; Bijective linear map; Nonlinear operator; Linear Schrödinger Operator; Vector space homomorphism; Vector space isomorphism; Linear extension of a function; Linear extension (linear algebra); Extend by linearity; Linear endomorphism

In mathematics, and more specifically in linear algebra, a linear map (also called a linear mapping, linear transformation, vector space homomorphism, or in some contexts linear function) is a mapping V \to W between two vector spaces that preserves the operations of vector addition and scalar multiplication. The same names and the same definition are also used for the more general case of modules over a ring; see Module homomorphism.

https://en.wikipedia.org/wiki/Linear_map

linear transformation

$The function f:\R^2 \to \R^2 with f(x, y) = (2x, y) is a linear map. This function scales the x component of a vector by the factor 2.$
$The function f(x, y) = (2x, y) is additive: It doesn't matter whether vectors are first added and then mapped or whether they are mapped and finally added: f(\mathbf a + \mathbf b) = f(\mathbf a) + f(\mathbf b)$
$The function f(x, y) = (2x, y) is homogeneous: It doesn't matter whether a vector is first scaled and then mapped or first mapped and then scaled: f(\lambda \mathbf a) = \lambda f(\mathbf a)$

MAPPING THAT PRESERVES THE OPERATIONS OF ADDITION AND SCALAR MULTIPLICATION

Linear operator; Linear mapping; Linear transformations; Linear operators; Linear transform; Linear maps; Linear isomorphism; Linear isomorphic; Linear Transformation; Linear Transformations; Linear Operator; Homogeneous linear transformation; User:The Uber Ninja/X3; Linear transformation; Bijective linear map; Nonlinear operator; Linear Schrödinger Operator; Vector space homomorphism; Vector space isomorphism; Linear extension of a function; Linear extension (linear algebra); Extend by linearity; Linear endomorphism

linear map

Associative algebra

ALGEBRA OVER A RING SUCH THAT MULTIPLICATION IS ASSOCIATIVE

Linear associative algebra; Abelian algebra; R-algebra; Associative Algebra; Associative algebras; Associative R-algebra; Commutative R-algebra; Commutative algebra (structure); Unital associative algebra; Draft:Associative algebra; Bidimension of an associative algebra; Wedderburn principal theorem; Enveloping algebra of an associative algebra

In mathematics, an associative algebra A is an algebraic structure with compatible operations of addition, multiplication (assumed to be associative), and a scalar multiplication by elements in some field K. The addition and multiplication operations together give A the structure of a ring; the addition and scalar multiplication operations together give A the structure of a vector space over K.

https://en.wikipedia.org/wiki/Associative_algebra

*-algebra

ALGEBRA EQUIPPED WITH AN INVOLUTION OVER A *-RING

Star algebra; *-homomorphism; * algebra; Involution algebra; Involutive algebra; *-ring; Star-algebra; * ring; Involutory ring; Involutary ring; Star ring; *algebra; Involutive ring

In mathematics, and more specifically in abstract algebra, a *-algebra (or involutive algebra) is a mathematical structure consisting of two involutive rings and , where is commutative and has the structure of an associative algebra over . Involutive algebras generalize the idea of a number system equipped with conjugation, for example the complex numbers and complex conjugation, matrices over the complex numbers and conjugate transpose, and linear operators over a Hilbert space and Hermitian adjoints.

https://en.wikipedia.org/wiki/*-algebra

Википедия

Linear algebra

Linear algebra is the branch of mathematics concerning linear equations such as:

a_{1}x_{1}+\cdots +a_{n}x_{n}=b,

linear maps such as:

(x_{1},\ldots ,x_{n})\mapsto a_{1}x_{1}+\cdots +a_{n}x_{n},

and their representations in vector spaces and through matrices.

Linear algebra is central to almost all areas of mathematics. For instance, linear algebra is fundamental in modern presentations of geometry, including for defining basic objects such as lines, planes and rotations. Also, functional analysis, a branch of mathematical analysis, may be viewed as the application of linear algebra to spaces of functions.

Linear algebra is also used in most sciences and fields of engineering, because it allows modeling many natural phenomena, and computing efficiently with such models. For nonlinear systems, which cannot be modeled with linear algebra, it is often used for dealing with first-order approximations, using the fact that the differential of a multivariate function at a point is the linear map that best approximates the function near that point.

https://en.wikipedia.org/wiki/Linear algebra