In algebra, the kernel of a homomorphism (function that preserves the structure) is generally the inverse image of 0 (except for groups whose operation...

Numerical Linear Algebra, SIAM, ISBN 978-0-89871-361-9. Wikibooks has a book on the topic of: Linear Algebra/Null Spaces "Kernel of a matrix", Encyclopedia...

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...

inequivalent irreducible representations with kernel K(H) or with kernel {0}. Suppose A is a finite-dimensional C*-algebra. It is known A is isomorphic to a finite...

mathematics, kernels are a generalization of the kernels of group homomorphisms, the kernels of module homomorphisms and certain other kernels from algebra. Intuitively...

would have three nested loops. Linear algebra programs have many common low-level operations (the so-called "kernel" operations, not related to operating...

In machine learning, kernel machines are a class of algorithms for pattern analysis, whose best known member is the support-vector machine (SVM). These...

preserving maps called homomorphisms are vital in the study of algebraic objects. Homomorphisms Kernels and cokernels Image and coimage Epimorphisms and monomorphisms...

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

In probability theory, a Markov kernel (also known as a stochastic kernel or probability kernel) is a map that in the general theory of Markov processes...

In set theory, the kernel of a function f {\displaystyle f} (or equivalence kernel) may be taken to be either the equivalence relation on the function's...

trivial kernel. An important example of such an algebra is a commutative C*-algebra. In fact, when A {\displaystyle A} is a commutative unital C*-algebra, the...

The spectrum of a commutative C*-algebra can also be viewed as the set of all maximal ideals m of A, with the hull-kernel topology. (See the earlier remarks...

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...

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...

In ring theory, a branch of abstract algebra, a quotient ring, also known as factor ring, difference ring or residue class ring, is a construction quite...

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

isomorphism of Lie algebras is a bijective homomorphism. As with normal subgroups in groups, ideals in Lie algebras are precisely the kernels of homomorphisms...

library of algorithms, efficient data structures and a fast kernel. These computer algebra systems are sometimes combined with "front end" programs that...

modules, Lie algebras, and other algebraic structures. In universal algebra, the isomorphism theorems can be generalized to the context of algebras and congruences...

also a group homomorphism. Its kernel is an algebraic subgroup of G {\displaystyle \mathrm {G} } , its image is an algebraic subgroup of G ′ {\displaystyle...

of S. The kernel of f, defined as ker(f) = {a in R | f(a) = 0S}, is a two-sided ideal in R. Every two-sided ideal in a ring R is the kernel of some ring...

kernels correspond to self-adjoint operators. There are many classes of problems that are difficult to solve—or at least quite unwieldy algebraically—in...

In mathematics, the exterior algebra or Grassmann algebra of a vector space V {\displaystyle V} is an associative algebra that contains V , {\displaystyle...

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 mathematics, rings are algebraic structures that generalize fields: multiplication need not be commutative and multiplicative inverses need not exist...

Homological algebra is the branch of mathematics that studies homology in a general algebraic setting. It is a relatively young discipline, whose origins...

called the corank of f. Cokernels are dual to the kernels of category theory, hence the name: the kernel is a subobject of the domain (it maps to the domain)...

included in the kernel of the next. Associated to a chain complex is its homology, which describes how the images are included in the kernels. A cochain complex...

A non-associative algebra (or distributive algebra) is an algebra over a field where the binary multiplication operation is not assumed to be associative...