Outer inverses and Jacobi type identities

Authors

Ravindra B. Bapat, Indian Statistical Institute (Delhi Centre)
Manjunatha Prasad Karantha, Manipal Academy of Higher Education
Nupur Nandini, Manipal Academy of Higher Education
Divya P. Shenoy, Manipal Academy of Higher Education

Article Type

Research Article

Publication Title

Linear Algebra and Its Applications

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.

First Page

274

Last Page

294

DOI

10.1016/j.laa.2017.09.025

Publication Date

1-1-2018

Comments

All Open Access, Bronze

Recommended Citation

Bapat, Ravindra B.; Karantha, Manjunatha Prasad; Nandini, Nupur; and Shenoy, Divya P., "Outer inverses and Jacobi type identities" (2018). Journal Articles. 1618.
https://digitalcommons.isical.ac.in/journal-articles/1618