flâneur

tensor.pdf

people.math.harvard.edu · 2,894 words · saved by 1 readers

N/A

Math 55a: Honors Abstract Algebra Tensor products Slogan. Tensor products of vector spaces are to Cartesian products of sets as direct sums of vector spaces are to disjoint unions of sets. Description. For any two vector spaces U, V over the same field F , we will construct a tensor product U ⊗ V (occasionally still known also as the “Kronecker product” of U and V ), which is also an F -vector space. If U, V are finite dimensional then so is U ⊗ V , with dim(U ⊗V ) = dim U ·dim V . If U has basis {ui : i ∈ I} and V has basis {vj : j ∈ J}, then U ⊗ V…

saved by

related reading