In mathematics, the kernel of a linear map, also known as the null space or nullspace, is the part of the domain which is mapped to the zero vector of...

In algebra, the kernel of a homomorphism is the relation describing how elements in the domain of the homomorphism become related in the image. A homomorphism...

Basic Linear Algebra Subprograms (BLAS) is a specification that prescribes a set of low-level routines for performing common linear algebra operations...

In linear algebra and functional analysis, a projection is a linear transformation P {\displaystyle P} from a vector space to itself (an endomorphism)...

Linear algebra is the branch of mathematics concerning linear equations such as a 1 x 1 + ⋯ + a n x n = b , {\displaystyle a_{1}x_{1}+\cdots +a_{n}x_{n}=b...

linear groups, projective groups, Euclidean groups, etc. Many matrix groups are also algebraic. Other algebraic groups occur naturally in algebraic geometry...

specifically in linear algebra, a linear map (also called a linear mapping, linear transformation, vector space homomorphism, or in some contexts linear function)...

system Kernel (algebra), a general concept that includes: Kernel (linear algebra) or null space, a set of vectors mapped to the zero vector Kernel (category...

The rank–nullity theorem is a theorem in linear algebra, which asserts: the number of columns of a matrix M is the sum of the rank of M and the nullity...

area of algebra, the projective linear group (also known as the projective general linear group or PGL) is the induced action of the general linear group...

In linear algebra, the rank of a matrix A is the dimension of the vector space generated (or spanned) by its columns. This corresponds to the maximal number...

analysis, ridge regression, spectral clustering, linear adaptive filters and many others. Most kernel algorithms are based on convex optimization or eigenproblems...

In linear algebra, the transpose of a matrix is an operator which flips a matrix over its diagonal; that is, it switches the row and column indices of...

functional analysis, a branch of mathematics, an operator algebra is an algebra of continuous linear operators on a topological vector space, with the multiplication...

resulting algebraic structure is a monoid, usually called the full linear monoid, but occasionally also full linear semigroup, general linear monoid etc...

matrix inversion. This is the normal subgroup of the general linear group given by the kernel of the determinant det : GL ⁡ ( n , R ) → R × . {\displaystyle...

(Terse) Introduction to Linear Algebra, American Mathematical Society, ISBN 978-0-8218-4419-9 Lax, Peter (1996), Linear algebra, Wiley-Interscience,...

In linear algebra, the quotient of a vector space V {\displaystyle V} by a subspace U {\displaystyle U} is a vector space obtained by "collapsing" U {\displaystyle...

In linear algebra, a linear relation, or simply relation, between elements of a vector space or a module is a linear equation that has these elements...

abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures...

and classification of Lie groups in terms of Lie algebras, which are simpler objects of linear algebra. In more detail: for any Lie group, the multiplication...

variables. Linear algebra is a closely related field that investigates linear equations and combinations of them called systems of linear equations. It...

pointwise operations and supremum norm) is a Banach algebra. The algebra of all continuous linear operators on a Banach space E {\displaystyle E} (with...

Intel oneAPI Math Kernel Library (Intel oneMKL), formerly known as Intel Math Kernel Library, is a library of optimized math routines for science, engineering...

ring, this notion of kernel coincides with the ordinary notion of a kernel of a homomorphism, if one identifies the ordinary kernel K of f: A → B with its...

In linear algebra, the minimal polynomial μA of an n × n {\displaystyle n\times n} matrix A over a field F is the monic polynomial P over F of least degree...

mathematics, a Clifford algebra is an algebra generated by a vector space with a quadratic form, and is a unital associative algebra with the additional structure...

but also a direction. The concept of vector spaces is fundamental for linear algebra, together with the concept of matrices, which allows computing in vector...

specifically in linear algebra, a linear subspace or vector subspace is a vector space that is a subset of some larger vector space. A linear subspace is...

In linear algebra, the trace of a square matrix A, denoted tr(A), is the sum of the elements on its main diagonal, a 11 + a 22 + ⋯ + a n n {\displaystyle...