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...

group Quotient space (linear algebra) – Vector space consisting of affine subsets Mapping cone (homological algebra) – Tool in homological algebra Brown...

as spaces. In particular: Quotient space (topology), in case of topological spaces Quotient space (linear algebra), in case of vector spaces Quotient space...

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

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...

concept of vector spaces is fundamental for linear algebra, together with the concept of matrices, which allows computing in vector spaces. This provides...

{\displaystyle M} is a closed linear subspace of a normed space X , {\displaystyle X,} there is a natural norm on the quotient space X / M , {\displaystyle X/M...

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

relation. Kernels allow defining quotient objects (also called quotient algebras in universal algebra). For many types of algebraic structure, the fundamental...

and to the quotient space in linear algebra. It is a specific example of a quotient, as viewed from the general setting of universal algebra. Starting...

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...

linear group of a vector space V on the associated projective space P(V). Explicitly, the projective linear group is the quotient group PGL(V) = GL(V) / Z(V)...

symmetric algebra over V can be viewed as a "coordinate free" polynomial ring over V. The symmetric algebra S(V) can be built as the quotient of the tensor...

topological space. A straightforward argument involving elementary linear algebra shows that the only finite-dimensional seminormed spaces are those arising...

structure, the quotient set often inherits a similar structure from its parent set. Examples include quotient spaces in linear algebra, quotient spaces in topology...

authors, especially in physics and matrix algebra, prefer to define inner products and sesquilinear forms with linearity in the second argument rather than the...

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

A particular case is that of a complex algebra A of continuous linear operators on a complex Hilbert space with two additional properties: A is a topologically...

In mathematics, a Lie algebra (pronounced /liː/ LEE) is a vector space g {\displaystyle {\mathfrak {g}}} together with an operation called the Lie bracket...

quotient rings of ring theory, quotient groups of group theory, the quotient spaces of linear algebra and the quotient modules of representation theory...

the following application to linear algebra. Let V be a finite-dimensional vector space over a field k and f : V → V a linear map with minimal polynomial...

functional analysis, the Calkin algebra, named after John Williams Calkin, is the quotient of B(H), the ring of bounded linear operators on a separable infinite-dimensional...

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

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

enveloping algebras are used in the representation theory of Lie groups and Lie algebras. For example, Verma modules can be constructed as quotients of the...

This normed quotient space is called Lebesgue space and it is the subject of this article. We begin by defining the quotient vector space. Given any f...

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

tensor algebra can be constructed as quotients: these include the exterior algebra, the symmetric algebra, the Clifford algebra, the Weyl algebra, and the...

vector space (called vectors). Abstract algebra is the name that is commonly given to the study of algebraic structures. The general theory of algebraic structures...

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...