tensor product

plural tensor products

1. mathematicsThe most general bilinear operation in various contexts (as with vectors, matrices, tensors, vector spaces, algebras, topological vector spaces, modules, and so on), denoted by ⊗.

   2 more examples

   Linear Transformations on Tensor Products of Vector Spaces [...] Proposition 16. Let V and W be finite dimensional vector spaces over the field F with bases v#95;1,...,v#95;n and w#95;1,...,w#95;m respectively. Then V#92;otimes#95;FW is a vector space over F of dimension nm with basis v#95;i#92;otimesw#95;j, 1#92;lei#92;len and 1#92;lej#92;lem.

   2004, David S. Dummit with Richard M. Foote, chapter 11, in Abstract Algebra, →ISBN, →OCLC, page 421

   [The tensor product] U#92;otimesV is the span of #92;#123;u#92;otimesv#58;u#92;inU,v#92;inV#92;#125; modulo the relations #92;begin#123;cases#125;#92;cdot#92;u#92;otimes(v#43;v')#61;u#92;otimesv#43;u#92;otimesv'#92;#92;#92;cdot#92;(u#43;u')#92;otimesv#61;u#92;otimesv#43;u'#92;otimesv#92;#92;#92;cdot#92;(#92;lambdau)#92;otimesv#61;#92;lambda(u#92;otimesv)#61;u#92;otimes(#92;lambdav)#92;end#123;cases#125;

   2012, 27:30 from the start, in Lecture 1 . Hopf Algebras and Combinatorics (Federico Ardila), spoken by Federico Ardila (Federico Ardila), Federico Ardila, via YouTube