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.
机构:
Sichuan Normal Univ, Coll Math & Software Sci, Chengdu 610066, Sichuan, Peoples R ChinaSichuan Normal Univ, Coll Math & Software Sci, Chengdu 610066, Sichuan, Peoples R China
Wang, Xue-ping
Shu, Qian-yu
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机构:
Sichuan Normal Univ, Coll Math & Software Sci, Chengdu 610066, Sichuan, Peoples R ChinaSichuan Normal Univ, Coll Math & Software Sci, Chengdu 610066, Sichuan, Peoples R China
机构:
Univ Ljubljana, Fac Math & Phys, Dept Math, Jadranska 19, SI-1000 Ljubljana, SloveniaUniv Ljubljana, Fac Math & Phys, Dept Math, Jadranska 19, SI-1000 Ljubljana, Slovenia