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...

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...

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...

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...

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 mathematics, a Malcev algebra (or Maltsev algebra or Moufang–Lie algebra) over a field is a nonassociative algebra that is antisymmetric, so that x...

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

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

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...

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...

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 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...

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

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...

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

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

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...

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

context of abstract algebra: The difference kernel of f and g is simply the kernel of the difference f − g. Furthermore, the kernel of a single function...

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

In mathematics, an associative algebra A over a commutative ring (often a field) K is a ring A together with a ring homomorphism from K into the center...

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

mathematics, and more specifically in abstract algebra, a *-algebra (or involutive algebra; read as "star-algebra") is a mathematical structure consisting of...

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...

In functional analysis, a branch of mathematics, the algebraic interior or radial kernel of a subset of a vector space is a refinement of the concept...

In mathematics, a ring is an algebraic structure consisting of a set with two binary operations called addition and multiplication, which obey the same...

denotes the kernel of the counit on A. This normality condition implies that HA+ is a Hopf ideal of H (i.e. an algebra ideal in the kernel of the counit...