Difference between revisions of "Tensor product"
Jump to navigation
Jump to search
| Line 1: | Line 1: | ||
{{WikiEntry|key=Tensor Product|qCode=1163016}} is a foundational operator in [[Linear Algebra]]. | {{WikiEntry|key=Tensor Product|qCode=1163016}} is a foundational operator in [[Linear Algebra]]. In mathematics, the tensor product V ⊗ W {\displaystyle V\otimes W} V\otimes W of two vector spaces V and W (over the same field) is a vector space to which is associated a bilinear map V × W → V ⊗ W , {\displaystyle V\times W\to V\otimes W,} {\displaystyle V\times W\to V\otimes W,} that maps a pair ( v , w ) , v ∈ V , w ∈ W {\displaystyle (v,w),\ v\in V,w\in W} {\displaystyle (v,w),\ v\in V,w\in W} to an element of V ⊗ W {\displaystyle V\otimes W} V\otimes W denoted v ⊗ w . {\displaystyle v\otimes w.} {\displaystyle v\otimes w.} | ||
[[Category:Linear Algebra]] | [[Category:Linear Algebra]] | ||
[[Category:Tensor Calculus]] | [[Category:Tensor Calculus]] | ||
[[Category:Category Theory]] | [[Category:Category Theory]] | ||
Revision as of 08:32, 20 March 2022
Tensor Product(Q1163016) is a foundational operator in Linear Algebra. In mathematics, the tensor product V ⊗ W {\displaystyle V\otimes W} V\otimes W of two vector spaces V and W (over the same field) is a vector space to which is associated a bilinear map V × W → V ⊗ W , {\displaystyle V\times W\to V\otimes W,} {\displaystyle V\times W\to V\otimes W,} that maps a pair ( v , w ) , v ∈ V , w ∈ W {\displaystyle (v,w),\ v\in V,w\in W} {\displaystyle (v,w),\ v\in V,w\in W} to an element of V ⊗ W {\displaystyle V\otimes W} V\otimes W denoted v ⊗ w . {\displaystyle v\otimes w.} {\displaystyle v\otimes w.}