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

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...

projective tensor product of two locally convex topological vector spaces is a natural topological vector space structure on their tensor product. Namely...

tensor product is the metric space completion of the ordinary tensor product. This is an example of a topological tensor product. The tensor product allows...

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

In mathematics, the injective tensor product of two topological vector spaces (TVSs) was introduced by Alexander Grothendieck and was used by him to define...

one also has the: Tensor product of Hilbert spaces Topological tensor product. The tensor product, outer product and Kronecker product all convey the same...

notions of tensor, and these various isomorphisms may or may not hold depending on what exactly is meant by a tensor (see topological tensor product). In some...

X{\widehat {\otimes }}_{\epsilon }Y} , the injective tensor product of the locally convex topological vector spaces (TVSs) X and Y. An integral linear operator...

intimately tied to the projective tensor product of two topological vector spaces (TVSs). Throughout let X,Y, and Z be topological vector spaces (TVSs) and L :...

The finest locally convex topological vector space (TVS) topology on X ⊗ Y , {\displaystyle X\otimes Y,} the tensor product of two locally convex TVSs...

and physics, a tensor field assigns a tensor to each point of a mathematical space (typically a Euclidean space or manifold). Tensor fields are used...

convex topological vector space, then the natural map from the projective tensor product of A and B {\displaystyle B} to the injective tensor product is an...

mathematical physics, a topological quantum field theory (or topological field theory or TQFT) is a quantum field theory which computes topological invariants. While...

In differential geometry, the tensor product of vector bundles E, F (over same space X {\displaystyle X} ) is a vector bundle, denoted by E ⊗ F, whose...

wikidata descriptions as a fallback Injective tensor product Nuclear operator – Linear operator related to topological vector spaces Nuclear space – A generalization...

Direct sum and the dual construction product Subspace and the dual construction quotient Topological tensor product Discrete space Locally constant function...

last themes, topological tensor products and regular configurations, were of more modest size than the others. Topological tensor products had played the...

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...

Topological tensor product – Tensor product constructions for topological vector spaces Nuclear operator – Linear operator related to topological vector...

relationship between the Ricci tensor and the matter content of the universe. Like the metric tensor, the Ricci tensor assigns to each tangent space of...

smash product of two pointed spaces (i.e. topological spaces with distinguished basepoints) (X, x0) and (Y, y0) is the quotient of the product space X...

on Hilbert spaces and use the term "nuclear operator" in more general topological vector spaces (such as Banach spaces). Note that the trace operator studied...

In mathematics, topological groups are the combination of groups and topological spaces, i.e. they are groups and topological spaces at the same time...

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

physics, topological order is a kind of order in the zero-temperature phase of matter (also known as quantum matter). Macroscopically, topological order...

In functional analysis, the Grothendieck trace theorem is an extension of Lidskii's theorem about the trace and the determinant of a certain class of nuclear...

inverse with respect to tensor product of sheaves of modules. It is the equivalent in algebraic geometry of the topological notion of a line bundle....

mathematical field of differential geometry, the Riemann curvature tensor or Riemann–Christoffel tensor (after Bernhard Riemann and Elwin Bruno Christoffel) is the...

processors, the first used a toric code with twist defects as a topological degenerancy (or topological defect) while the second used a different but related protocol...