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

injective tensor product is a particular topological tensor product, a topological vector space (TVS) formed by equipping the tensor product of the underlying...

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...

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, ...), and general relativity (stress–energy tensor, curvature tensor, ...). In...

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

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...

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

}_{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...

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 →...

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

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

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

topology that turns it into a topological tensor product, the most common of which are the projective tensor product, denoted by L p ( Ω , Σ , μ ) ⊗ π E ,...

completion of the injective tensor product (which in this case is identical to the completion of the projective tensor product). The inclusion map In : D...

{\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...

theories Nuclear operator Nuclear space Parafactorial local ring Projective tensor product Proper morphism – in algebraic geometry, an analogue of a proper...

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

A^{\prime }\otimes B\to \operatorname {Hom} (A,B)} (from the projective tensor product of A {\displaystyle A} and B {\displaystyle B} to the Banach space...

Injective tensor product Nuclear space – A generalization of finite-dimensional Euclidean spaces different from Hilbert spaces Projective tensor product – tensor...

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...

finite-dimensional Euclidean spaces different from Hilbert spaces Projective tensor product – tensor product defined on two topological vector spacesPages displaying...

algebraic tensor product X ⊗ Y {\displaystyle X\otimes Y} equipped with the projective tensor norm, and similarly for the injective tensor product X ⊗ ^ ε...

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

first-generation Tensor chip debuted on the Pixel 6 smartphone series in 2021, and was succeeded by the Tensor G2 chip in 2022, G3 in 2023 and G4 in 2024. Tensor has...

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...

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

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...

finite-dimensional Euclidean spaces different from Hilbert spaces Projective tensor product – tensor product defined on two topological vector spacesPages displaying...