Generalized inverses over integral domains

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

Research output: Contribution to journalArticle

41 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

Fingerprint

Integral domain
Generalized Inverse
Linear Combination
Minor
Principal ideal domain
If and only if
Moore-Penrose Inverse
Sum of squares
Invertible
Rank of a matrix

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Numerical Analysis

Cite this

Bapat, R. B. ; Bhaskara Rao, K. P S ; Prasad, K. Manjunatha. / Generalized inverses over integral domains. In: Linear Algebra and Its Applications. 1990 ; Vol. 140, No. C. pp. 181-196.
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Generalized inverses over integral domains. / Bapat, R. B.; Bhaskara Rao, K. P S; Prasad, K. Manjunatha.

In: Linear Algebra and Its Applications, Vol. 140, No. C, 15.10.1990, p. 181-196.

Research output: Contribution to journalArticle

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