mathematics, the tensor product of two algebras over a commutative ring R is also an R-algebra. This gives the tensor product of algebras. When the ring...

tensor algebra of a vector space V, denoted T(V) or T•(V), is the algebra of tensors on V (of any rank) with multiplication being the tensor product....

v\otimes w} is called the tensor product of v and w. An element of V ⊗ W {\displaystyle V\otimes W} is a tensor, and the tensor product of two vectors is sometimes...

abstract algebra. The tensor product of an algebra and a module can be used for extension of scalars. For a commutative ring, the tensor product of modules...

R-algebras. Tensor products The tensor product of two R-algebras is also an R-algebra in a natural way. See tensor product of algebras for more details...

In mathematics, the tensor product of two fields is their tensor product as algebras over a common subfield. If no subfield is explicitly specified, the...

glossary of tensor theory. For expositions of tensor theory from different points of view, see: Tensor Tensor (intrinsic definition) Application of tensor theory...

Tensor product of Hilbert spaces, endowed with a special inner product as to remain a Hilbert space Other topological tensor products Tensor product of...

category of commutative algebras over a commutative ring is a tensor product of algebras. A coproduct in the category of algebras is a free product of algebras...

that the Weyl algebra is a quantization of the symmetric algebra. Weyl algebras and Clifford algebras admit a further structure of a *-algebra, and can be...

mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects related to a vector space. Tensors may map...

}(V).} In particular, the exterior algebra of a direct sum is isomorphic to the tensor product of the exterior algebras: ⋀ ( V ⊕ W ) ≅ ⋀ ( V ) ⊗ ⋀ ( W )...

In multilinear algebra, a tensor contraction is an operation on a tensor that arises from the canonical pairing of a vector space and its dual. In components...

component-free approach to the theory of a tensor views a tensor as an abstract object, expressing some definite type of multilinear concept. Their properties...

The outer product of tensors is also referred to as their tensor product, and can be used to define the tensor algebra. The outer product contrasts with:...

analysis, the tensor product of Hilbert spaces is a way to extend the tensor product construction so that the result of taking a tensor product of two Hilbert...

space tensor product of two Hilbert spaces is the completion of their algebraic tensor product. One can define a tensor product of von Neumann algebras (a...

define a free product of two algebras. Let A and B be algebras over a commutative ring R. Consider their tensor algebra, the direct sum of all possible...

product Outer product Kronecker delta Levi-Civita symbol Multilinear form Pseudoscalar Pseudovector Spinor Tensor Tensor algebra, Free algebra Tensor...

objects (also called quotient algebras in universal algebra, and cokernels in category theory). For many types of algebraic structure, the fundamental theorem...

In mathematics, the tensor product of representations is a tensor product of vector spaces underlying representations together with the factor-wise group...

the category of R-algebras to the category of sets. Free algebras over division rings are free ideal rings. Cofree coalgebra Tensor algebra Free object...

a tensor field is a function assigning a tensor to each point of a region of a mathematical space (typically a Euclidean space or manifold) or of the...

algebra over K that splits over L and such that deg A = [L : K] arises in this way. The tensor product of algebras corresponds to multiplication of the...

of a field K is an abelian group whose elements are Morita equivalence classes of central simple algebras over K, with addition given by the tensor product...

with a group operation given by the tensor product of algebras. The resulting group is called the Brauer group Br(F) of the field F. It is always a torsion...

K and addition is induced by the tensor product of algebras. It arose out of attempts to classify division algebras over a field and is named after the...

infinite-dimensional Lie algebra over R {\displaystyle \mathbb {R} } . The Kac–Moody algebras are a large class of infinite-dimensional Lie algebras, say over C {\displaystyle...

specifically multilinear algebra, a dyadic or dyadic tensor is a second order tensor, written in a notation that fits in with vector algebra. There are numerous...

algebras of pseudo-differential operators acting on spaces of distributions), the term operator algebra is usually used in reference to algebras of bounded...