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Determinantal Representations of the Quaternion Core Inverse and Its Generalizations

  • Ivan KyrcheiEmail author
Article
  • 43 Downloads

Abstract

In this paper, we extend notions of the core inverse, core-EP inverse, DMP inverse, and CMP inverse over the quaternion skew field \({\mathbb {H}}\) that have some features in comparison to complex matrices. We give the direct method of their computing, namely, their determinantal representations by using column and row noncommutative determinants previously introduced by the author. As the special case, we give their determinantal representations for complex matrices as well. A numerical example to illustrate the main result is given.

Keywords

Core inverse Core-EP inverse Generalized inverse Moore–Penrose inverse Drazin inverse Quaternion matrix Noncommutative determinant 

Mathematics Subject Classification

Primary 15A09 Secondary 15A15 15B33 

Notes

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Pidstrygach Institute for Applied Problems of Mechanics and Mathematics of NAS of UkraineLvivUkraine

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