Generalized inverses of matrices over commutative rings

Research output: Contribution to journalArticle

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

Fingerprint

Generalized Inverse
Commutative Ring
Idempotent
Group Inverse
Minor
If and only if
Necessary Conditions
Computing
Sufficient Conditions

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Numerical Analysis

Cite this

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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.",
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Generalized inverses of matrices over commutative rings. / Manjunatha Prasad, K.

In: Linear Algebra and Its Applications, Vol. 211, No. C, 01.11.1994, p. 35-52.

Research output: Contribution to journalArticle

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