Linear preservers of term ranks of matrices over semirings

被引:11
|
作者
Kang, Kyung-Tae [1 ]
Song, Seok-Zun [1 ]
Beasley, LeRoy B. [2 ]
机构
[1] Cheju Natl Univ, Dept Math, Cheju 690756, South Korea
[2] Utah State Univ, Dept Math & Stat, Logan, UT 84322 USA
基金
新加坡国家研究基金会;
关键词
Semiring; Term rank; Covering; Linear operator;
D O I
10.1016/j.laa.2011.08.046
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The term rank of a matrix A over a semiring S is the least number of lines (rows or columns) needed to include all the nonzero entries in A. In this paper, we study linear operators that preserve term ranks of matrices over S. In particular, we show that a linear operator Ton matrix space over S preserves term rank if and only if T preserves term ranks 1 and alpha(>= 2) if and only if T preserves two consecutive term ranks in a restricted condition. Other characterizations of term-rank preservers are also given. (C) 2011 Elsevier Inc. All rights reserved.
引用
收藏
页码:1850 / 1862
页数:13
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