Preservers of term ranks of symmetric matrices

被引：7

作者：

Beasley, LeRoy B. ^{[2
]}

Song, Seok-Zun ^{[1
]}

Kang, Kyung-Tae ^{[1
]}

机构：

[1] Cheju Natl Univ, Dept Math, Cheju 690756, South Korea

[2] Utah State Univ, Dept Math & Stat, Logan, UT 84322 USA

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2012年 / 436卷 / 06期

基金：

新加坡国家研究基金会;

关键词：

Semiring; Term rank; Symmetric matrix; Linear operator;

D O I：

10.1016/j.laa.2011.06.018

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The term rank of an n x n matrix A 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 n x n symmetric matrices with entries in a commutative antinegative semiring S and with all diagonal entries zero. Consequently, we show that a linear operator T on symmetric matrices with zero diagonal preserves term rank if and only if T preserves term ranks 2 and k (>= 3) if and only if T preserves term ranks 3 and k (>= 4). Other characterizations of term-rank preservers are also given. (C) 2011 Elsevier Inc. All rights reserved.

引用

页码：1727 / 1738

页数：12