Outer inverses and Jacobi type identities

Ravindra B. Bapat, Manjunatha Prasad Karantha, Nupur Nandini, Divya P. Shenoy

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Abstract

We consider matrices over a commutative ring and characterize the class of outer inverses for which Jacobi type identities can be extended. We obtain a necessary and sufficient condition for the existence of Rao-regular Drazin inverse in terms of sum of principal minors of Ak for some k. Also, we obtain determinantal formula for the Rao-regular Drazin inverse. Conjectures are formulated which give expressions for outer inverse and the conjectures are proved in some special cases.

Original languageEnglish
Pages (from-to)274-294
Number of pages21
JournalLinear Algebra and Its Applications
Volume536
DOIs
Publication statusPublished - 01-01-2018

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All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

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