### Abstract

A Rao-regular matrix and the Rao idempotent of a matrix over a commutative ring are defined. We prove that a matrix A over a commutative ring is regular if and only if A is a sum of Rao-regular matrices with mutually orthogonal Rao idempotents. We find necessary and sufficient conditions for a matrix to have group inverse over a commutative ring. Also, we give a method for computing minors of reflexive g-inverse whenever it exists.

Original language | English |
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Pages (from-to) | 35-52 |

Number of pages | 18 |

Journal | Linear Algebra and Its Applications |

Volume | 211 |

Issue number | C |

DOIs | |

Publication status | Published - 01-11-1994 |

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### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory
- Numerical Analysis

### Cite this

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*Linear Algebra and Its Applications*, vol. 211, no. C, pp. 35-52. https://doi.org/10.1016/0024-3795(94)90081-7

**Generalized inverses of matrices over commutative rings.** / Manjunatha Prasad, K.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Generalized inverses of matrices over commutative rings

AU - Manjunatha Prasad, K.

PY - 1994/11/1

Y1 - 1994/11/1

N2 - A Rao-regular matrix and the Rao idempotent of a matrix over a commutative ring are defined. We prove that a matrix A over a commutative ring is regular if and only if A is a sum of Rao-regular matrices with mutually orthogonal Rao idempotents. We find necessary and sufficient conditions for a matrix to have group inverse over a commutative ring. Also, we give a method for computing minors of reflexive g-inverse whenever it exists.

AB - A Rao-regular matrix and the Rao idempotent of a matrix over a commutative ring are defined. We prove that a matrix A over a commutative ring is regular if and only if A is a sum of Rao-regular matrices with mutually orthogonal Rao idempotents. We find necessary and sufficient conditions for a matrix to have group inverse over a commutative ring. Also, we give a method for computing minors of reflexive g-inverse whenever it exists.

UR - http://www.scopus.com/inward/record.url?scp=0038836526&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0038836526&partnerID=8YFLogxK

U2 - 10.1016/0024-3795(94)90081-7

DO - 10.1016/0024-3795(94)90081-7

M3 - Article

VL - 211

SP - 35

EP - 52

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

IS - C

ER -