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 (function that preserves the structure) is generally the inverse image of 0 (except for groups whose operation...

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...

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...

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...

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...

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...

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...

conjugate transpose, and linear operators over a Hilbert space and Hermitian adjoints. However, it may happen that an algebra admits no involution. Look...

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...

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

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

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

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

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

(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 transpose of a linear map between two vector spaces, defined over the same field, is an induced map between the dual spaces of...

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

In linear algebra, the minimal polynomial μA of an n × n matrix A over a field F is the monic polynomial P over F of least degree such that P(A) = 0. Any...

In mathematics, a linear algebraic group is a subgroup of the group of invertible n × n {\displaystyle n\times n} matrices (under matrix multiplication)...

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

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...

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...

the algebraic dual space. When defined for a topological vector space, there is a subspace of the dual space, corresponding to continuous linear functionals...

In linear algebra, the column space (also called the range or image) of a matrix A is the span (set of all possible linear combinations) of its column...

{coker} T\to 0.} These can be interpreted thus: given a linear equation T(v) = w to solve, the kernel is the space of solutions to the homogeneous equation...