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On a new generalized inverse for matrices of an arbitrary index

Authors
Journal
Applied Mathematics and Computation
0096-3003
Publisher
Elsevier
Publication Date
Identifiers
DOI: 10.1016/j.amc.2013.10.060
Keywords
  • Moore–Penrose Inverse
  • Drazin Inverse
  • Index
  • Core Inverse
Disciplines
  • Mathematics

Abstract

Abstract The purpose of this paper is to introduce a new generalized inverse, called DMP inverse, associated with a square complex matrix using its Drazin and Moore–Penrose inverses. DMP inverse extends the notion of core inverse, introduced by Baksalary and Trenkler for matrices of index at most 1 in (Baksalary and Trenkler (2010) [1]) to matrices of an arbitrary index. DMP inverses are analyzed from both algebraic as well as geometrical approaches establishing the equivalence between them.

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