Generalized inverses over integral domains

R. B. Bapat, K. P S Bhaskara Rao, K. Manjunatha Prasad

Research output: Contribution to journalArticle

45 Citations (Scopus)

Abstract

In an earlier paper one of the authors showed that a matrix of rank r over an integral domain has a generalized inverse if and only if a linear combination of all the r × r minors of the matrix is one. In the same paper a procedure for constructing a generalized inverse from such a linear combination was also given. In the present paper we show that any reflexive generalized inverse can be obtained by that procedure. We also show that if the integral domain is a principal ideal domain, every generalized inverse can be obtained by that procedure. It is also shown that a matrix A of rank r over an integral domain has Moore-Penrose inverse if and only if the sum of squares of all r × r minors of A is an invertible element of the integral domain.

Original languageEnglish
Pages (from-to)181-196
Number of pages16
JournalLinear Algebra and Its Applications
Volume140
Issue numberC
DOIs
Publication statusPublished - 15-10-1990

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Numerical Analysis

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