Linear preservers of matrices of rank-2 |
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| Authors: | Leroy B Beasley Thomas J Laffey |
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| Institution: | 1. Department ofMathematics , Utah State University , Logan, Utah, 84322-3900, USA lbeeasley@sunfs.math.usu.edu;3. Department of Mathematics , University College Dublin , Dublin 4, Dublin, Ireland |
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| Abstract: | Let T be a linear operator on the space of all m×n matrices over any field. we prove that if T maps rank-2 matrices to rank-2 matrices then there exist nonsingular matrices U and V such that either T(X)=UXV for all matrices X, or m=n and T(X)=UXtV for all matrices X where Xt denotes the transpose of X. |
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| Keywords: | Preserver Rank (U-K)-operator AMS Classifications: 15A04 15A33 |
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