Linear preservers of matrices of rank-2

被引：5
|
作者：
Beasley, LB [1 ]
Laffey, TJ
机构：
[1] Utah State Univ, Dept Math, Logan, UT 84322 USA
[2] Natl Univ Ireland Univ Coll Dublin, Dept Math, Dublin 4, Ireland
来源：
LINEAR & MULTILINEAR ALGEBRA | 2001年 / 48卷 / 04期
关键词：
preserver; rank; (U-V)-operator;
D O I：
10.1080/03081080108818678
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let T be a linear operator on the space of all m x 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) = UX V for all matrices X, or m = n and T(X) = (UXV)-V-t for all matrices X where X-t denotes the transpose of X.
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页码：319 / 331
页数：13
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