Generalized inverses over integral domains. II. group inverses and Drazin inverses

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

Research output: Contribution to journalArticle

20 Citations (Scopus)

Abstract

This is a continuation of an earlier paper by the authors on generalized inverses over integral domains. The main results consist of necessary and sufficient conditions for the existence of a group inverse, a new formula for a group inverse when it exists, and necessary and sufficient conditions for the existence of a Drazin inverse. We show that a square matrix A of rank r over an integral domain R has a group inverse if and only if the sum of all r × r principal minors of A is an invertible element of R. We also show that the group inverse of A when it exists is a polynomial in A with coefficients from R.

Original languageEnglish
Pages (from-to)31-47
Number of pages17
JournalLinear Algebra and Its Applications
Volume146
Issue numberC
DOIs
Publication statusPublished - 15-02-1991

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Group Inverse
Drazin Inverse
Integral domain
Generalized Inverse
Polynomials
Necessary Conditions
Sufficient Conditions
Square matrix
Invertible
Continuation
Minor
If and only if
Polynomial
Coefficient

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Numerical Analysis

Cite this

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Generalized inverses over integral domains. II. group inverses and Drazin inverses. / Manjunatha Prasad, K.; Bhaskara Rao, K. P S; Bapat, R. B.

In: Linear Algebra and Its Applications, Vol. 146, No. C, 15.02.1991, p. 31-47.

Research output: Contribution to journalArticle

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