Projective tensor product information

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

completions of the algebraic tensor product in these two norms are called the projective and injective tensor products, and are denoted by A ⊗ ^ π ⁡...

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...

(from scratch) a topology on such a tensor product is frequently equivalent to the injective or projective tensor product topology. Let U {\displaystyle {\mathfrak...

In mathematics, the tensor product of modules is a construction that allows arguments about bilinear maps (e.g. multiplication) to be carried out in terms...

(electromagnetic tensor, Maxwell tensor, permittivity, magnetic susceptibility, ...), general relativity (stress–energy tensor, curvature tensor, ...), and...

doctoral dissertation. Nuclear operators are intimately tied to the projective tensor product of two topological vector spaces (TVSs). Throughout let X,Y, and...

}_{i_{r+p}}.} The components of this tensor are precisely the skew part of the components of the tensor product s ⊗ t, denoted by square brackets on the...

Tensor networks or tensor network states are a class of variational wave functions used in the study of many-body quantum systems. Tensor networks extend...

{\displaystyle n} and a tensor of order m {\displaystyle m} is a tensor of order n + m − 2 {\displaystyle n+m-2} , see Tensor contraction for details...

TVSs, let X ⊗ π Y {\displaystyle X\otimes _{\pi }Y} denote the projective tensor product, X ⊗ ^ π Y {\displaystyle X{\widehat {\otimes }}_{\pi }Y} denote...

differential geometry, the torsion tensor is a tensor that is associated to any affine connection. The torsion tensor is bilinear map of two input vectors...

_{1}\right)} is nuclear, this tensor product is simultaneously the injective tensor product and projective tensor product). In short, the Schwartz kernel...

In mathematics, a symmetric tensor is a tensor that is invariant under a permutation of its vector arguments: T ( v 1 , v 2 , … , v r ) = T ( v σ 1 , v...

complex projective space is the projective space with respect to the field of complex numbers. By analogy, whereas the points of a real projective space...

vector space (TVS) topology on X ⊗ Y , {\displaystyle X\otimes Y,} the tensor product of two locally convex TVSs, making the canonical map ⋅ ⊗ ⋅ : X × Y →...

calculus Tensor product Product topology Cap product Cup product Slant product Smash product Wedge sum (or wedge product) Internal product, in a monoidal...

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...

projective modules, and, over a principal ideal domain, torsion free modules. Formally, a module M over a ring R is flat if taking the tensor product...

functions. In the language of tensor algebra, a particular tensor is associated with a particular shape with many lines projecting upwards and downwards, corresponding...

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

Multilinear algebra Tensor Classical treatment of tensors Component-free treatment of tensors Gamas's Theorem Outer product Tensor algebra Exterior algebra...

Matrix Product States and Projected Entangled Pair States Hand-waving and Interpretive Dance: An Introductory Course on Tensor Networks Tensor Networks...

Segre embedding is used in projective geometry to consider the cartesian product (of sets) of two projective spaces as a projective variety. It is named after...

a Cartesian tensor uses an orthonormal basis to represent a tensor in a Euclidean space in the form of components. Converting a tensor's components from...

consequently a vector is called a contravariant tensor. A vector, which is an example of a contravariant tensor, has components that transform inversely to...

tensor (symbol σ {\displaystyle {\boldsymbol {\sigma }}} , named after Augustin-Louis Cauchy), also called true stress tensor or simply stress tensor...