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Linear transformations
of tensor products preserving a fixed rank
Dragomir Z. Djokovic |
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Vol. 30 (1969), No. 2, 411–414
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Abstract |
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In this paper T is a linear transformation from a tensor product X⊗ Yinto 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 < dimU,k < dimV ) such that whenever z ∈ X ⊗ Y has rank k then also Tz ∈ U ⊗ V has rank k. It is shown that T = A ⊗ B or T = S ∘ (C ⊗ D) where A,B,C,D are appropriate linear isomorphisms and S is the canonical isomorphism of V ⊗ U onto U ⊗ V . |
Mathematical Subject Classification
Primary: 15.80
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Milestones
Received: 21 August 1968
Published: 1 August 1969
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Authors |
| Dragomir Z. Djokovic | |
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