Regular matrices and their strong preservers over semirings期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Regular matrices and their strong preservers over semirings

Authors:	Seok-Zun Song Kyung-Tae Kang LeRoy B Beasley Nung-Sing Sze

Affiliation:	^aDepartment of Mathematics, Cheju National University, Jeju 690-756, Republic of Korea ^bDepartment of Mathematics and Statistics, Utah State University, Logan, UT 84322-3900, USA ^cDepartment of Mathematics, University of Connecticut, Storrs, CT 06269-3009, USA

Abstract:	An m×n matrix A over a semiring is called regular if there is an n×m matrix G over such that AGA=A. We study the problem of characterizing those linear operators T on the matrices over a semiring such that T(X) is regular if and only if X is. Complete characterizations are obtained for many semirings including the Boolean algebra, the nonnegative reals, the nonnegative integers and the fuzzy scalars.

Keywords:	Semiring Generalized inverse of a matrix Regular matrix Linear operator
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