Vol. 30, No. 2, 1969

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Linear transformations of tensor products preserving a fixed rank

Dragomir Z. Djokovic

Vol. 30 (1969), No. 2, 411–414
Abstract

In this paper T is a linear transformation from a tensor product XYinto 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
Milestones
Received: 21 August 1968
Published: 1 August 1969
Authors
Dragomir Z. Djokovic