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 publicationJournal articleAcademic researchpeer-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 languageEnglish
Pages (from-to)209-223
Number of pages15
JournalLinear Algebra and Its Applications
Volume429
Issue number1
DOIs
Publication statusPublished - 1 Jul 2008
Externally publishedYes

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

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