Linear transformations of tensor products preserving a fixed rank
1969; Mathematical Sciences Publishers; Volume: 30; Issue: 2 Linguagem: Inglês
10.2140/pjm.1969.30.411
ISSN1945-5844
Autores Tópico(s)Tensor decomposition and applications
ResumoIn this paper T is a linear transformation from a tensor product X® Finto U® V, where X, Y, U,V are vector spaces over an infinite field F. The main result gives a characterization of surjective transformations T for which there is a positive integer k(k < dim U,k< dim V) such that whenever zeX®Y has rank k then also TzeU®V has rank k.It is shown that T = A®B or T = So (C D) where A, 5, C, D are appropriate linear isomorphisms and S is the canonical isomorphism of V® U onto U®V.
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