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 spaces...

In mathematics, the tensor product V ⊗ W {\displaystyle V\otimes W} of two vector spaces V {\displaystyle V} and W {\displaystyle W} (over the same field)...

topological tensor product of two topological vector spaces. For Hilbert spaces or nuclear spaces there is a simple well-behaved theory of tensor products (see...

spaces of V and W. For infinite-dimensional vector spaces, one also has the: Tensor product of Hilbert spaces Topological tensor product. The tensor product...

product space (or, rarely, a Hausdorff pre-Hilbert space) is a real vector space or a complex vector space with an operation called an inner product....

exactly is meant by a tensor (see topological tensor product). In some applications, it is the tensor product of Hilbert spaces that is intended, whose...

spaces, examples of Hilbert spaces include spaces of square-integrable functions, spaces of sequences, Sobolev spaces consisting of generalized functions...

product (matrices) Hilbert–Schmidt inner product Kronecker product Matrix analysis Matrix multiplication Matrix norm Tensor product of Hilbert spaces...

two Hilbert spaces is defined to be the von Neumann algebra generated by their algebraic tensor product, considered as operators on the Hilbert space tensor...

} From the formulas above, the Hilbert–Poincaré series of a direct sum and of a tensor product of graded vector spaces (finite dimensional in each degree)...

vector spaces and allows a concrete representation Tensor product of Hilbert spaces, endowed with a special inner product as to remain a Hilbert space Other...

antisymmetrized tensor product of n single-particle Hilbert spaces H (see symmetric algebra and exterior algebra respectively). A general state in Fock space is a...

tensor product of spin states from finite dimensional Hilbert spaces and the wavefunction which was previously developed. The basis for this Hilbert space...

the ring Z of integers). The construction may also be extended to cover Banach spaces and Hilbert spaces. See the article decomposition of a module for...

tensor product of complete spaces is not complete again. When working with Banach spaces, it is customary to say that the projective tensor product of...

the tensor product of Hilbert spaces H ∗ ⊗ H , {\displaystyle H^{*}\otimes H,} where H∗ is the dual space of H. The norm induced by this inner product is...

of topological vector spaces, which include function spaces, inner product spaces, normed spaces, Hilbert spaces and Banach spaces. In this article, vectors...

tensor product defined on two topological vector spacesPages displaying wikidata descriptions as a fallback Tensor product of Hilbert spaces – Tensor product...

topology Inductive tensor product Injective tensor product Projective tensor product Tensor product of Hilbert spaces Topological tensor product Émery topology...

embedding of the Cartesian product of two projective spaces into the projective space associated to the tensor product of the two Hilbert spaces, given by...

an area of mathematics, the projective tensor product of two locally convex topological vector spaces is a natural topological vector space structure...

Projective tensor product – a tensor product defined on two topological vector spaces Rigged Hilbert space – a construction linking the study of "bound"...

derivative of the coordinate functions xμ. These quantities evaluated at a point p provide a basis for the cotangent space at p. The tensor product (denoted...

differential geometry, a tensor density or relative tensor is a generalization of the tensor field concept. A tensor density transforms as a tensor field when passing...

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...

composed of two subsystems described in V and W respectively, then the Hilbert space of the entire system is the tensor product of the two spaces. (The exception...

dimension. In Hilbert spaces such operators are usually called trace class operators and one can define such things as the trace. In Banach spaces this is no...

space of X ⊗ ^ ϵ Y {\displaystyle X{\widehat {\otimes }}_{\epsilon }Y} , the injective tensor product of the locally convex topological vector spaces...

Hilbert C*-modules are mathematical objects that generalise the notion of Hilbert spaces (which are themselves generalisations of Euclidean space), in...

topological vector spacesPages displaying wikidata descriptions as a fallback Tensor product of Hilbert spaces – Tensor product space endowed with a special...