Regular matrices and their strong preservers over semirings

Seok Zun Song; Kyung Tae Kang; Le Roy B. Beasley; Nung Sing Sze

doi:10.1016/j.laa.2008.02.015

Regular matrices and their strong preservers over semirings

Seok Zun Song, Kyung Tae Kang, Le Roy B. Beasley, Nung Sing Sze

Research output: Journal article publication › Journal article › Academic research › peer-review

12 Citations (Scopus)

Abstract

An m × n matrix A over a semiring S is called regular if there is an n × m matrix G over S 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.

Original language	English
Pages (from-to)	209-223
Number of pages	15
Journal	Linear Algebra and Its Applications
Volume	429
Issue number	1
DOIs	https://doi.org/10.1016/j.laa.2008.02.015
Publication status	Published - 1 Jul 2008
Externally published	Yes

Keywords

Generalized inverse of a matrix
Linear operator
Regular matrix
Semiring

ASJC Scopus subject areas

Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics

More information

10.1016/j.laa.2008.02.015

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AU - Beasley, Le Roy B.

AU - Sze, Nung Sing

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AB - An m × n matrix A over a semiring S is called regular if there is an n × m matrix G over S 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.

KW - Generalized inverse of a matrix

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KW - Semiring

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Regular matrices and their strong preservers over semirings

Abstract

Keywords

ASJC Scopus subject areas

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