Manjunatha Prasad, K. ; Bhaskara Rao, K. P. S. ; Bapat, R. B.
(1991)
*Generalized inverses over integral domains. II. Group inverses and Drazin inverses*
Linear Algebra and its Applications, 146
.
pp. 31-47.
ISSN 0024-3795

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Official URL: http://www.sciencedirect.com/science/article/pii/0...

Related URL: http://dx.doi.org/10.1016/0024-3795(91)90018-R

## 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.

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ID Code: | 77804 |

Deposited On: | 14 Jan 2012 15:25 |

Last Modified: | 14 Jan 2012 15:25 |

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