Generalized inverses of matrices over commutative rings

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14 Citations (Scopus)

Abstract

A Rao-regular matrix and the Rao idempotent of a matrix over a commutative ring are defined. We prove that a matrix A over a commutative ring is regular if and only if A is a sum of Rao-regular matrices with mutually orthogonal Rao idempotents. We find necessary and sufficient conditions for a matrix to have group inverse over a commutative ring. Also, we give a method for computing minors of reflexive g-inverse whenever it exists.

Original languageEnglish
Pages (from-to)35-52
Number of pages18
JournalLinear Algebra and Its Applications
Volume211
Issue numberC
DOIs
Publication statusPublished - 01-11-1994

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Numerical Analysis

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