### Abstract

The theory of ‘minus partial order’ on the class of matrices over a field is well studied in the literature, and it is known that the rank additive property ‘ (Formula presented.) ’ holds whenever (Formula presented.) is lesser than (Formula presented.) under the minus partial order. The rank additive property fails in the class of regular matrices over a commutative ring, though several other characterizations of minus partial order relation known for the class of matrices over a field are easily extended. So, an extension of rank additive property in the class of regular matrices is further investigated. In the process, Rao–Mitra’s theorem on invariance of (Formula presented.) is further probed and a general condition for such invariance is obtained for matrices over a commutative ring.

Original language | English |
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Pages (from-to) | 929-941 |

Number of pages | 13 |

Journal | Linear and Multilinear Algebra |

Volume | 64 |

Issue number | 5 |

DOIs | |

Publication status | Published - 03-05-2016 |

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### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory

### Cite this

*Linear and Multilinear Algebra*,

*64*(5), 929-941. https://doi.org/10.1080/03081087.2015.1067667

}

*Linear and Multilinear Algebra*, vol. 64, no. 5, pp. 929-941. https://doi.org/10.1080/03081087.2015.1067667

**Minus partial order on regular matrices.** / Karantha, Manjunatha Prasad; Mohana; Shenoy, P. Divya.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Minus partial order on regular matrices

AU - Karantha, Manjunatha Prasad

AU - Mohana,

AU - Shenoy, P. Divya

PY - 2016/5/3

Y1 - 2016/5/3

N2 - The theory of ‘minus partial order’ on the class of matrices over a field is well studied in the literature, and it is known that the rank additive property ‘ (Formula presented.) ’ holds whenever (Formula presented.) is lesser than (Formula presented.) under the minus partial order. The rank additive property fails in the class of regular matrices over a commutative ring, though several other characterizations of minus partial order relation known for the class of matrices over a field are easily extended. So, an extension of rank additive property in the class of regular matrices is further investigated. In the process, Rao–Mitra’s theorem on invariance of (Formula presented.) is further probed and a general condition for such invariance is obtained for matrices over a commutative ring.

AB - The theory of ‘minus partial order’ on the class of matrices over a field is well studied in the literature, and it is known that the rank additive property ‘ (Formula presented.) ’ holds whenever (Formula presented.) is lesser than (Formula presented.) under the minus partial order. The rank additive property fails in the class of regular matrices over a commutative ring, though several other characterizations of minus partial order relation known for the class of matrices over a field are easily extended. So, an extension of rank additive property in the class of regular matrices is further investigated. In the process, Rao–Mitra’s theorem on invariance of (Formula presented.) is further probed and a general condition for such invariance is obtained for matrices over a commutative ring.

UR - http://www.scopus.com/inward/record.url?scp=84937785180&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84937785180&partnerID=8YFLogxK

U2 - 10.1080/03081087.2015.1067667

DO - 10.1080/03081087.2015.1067667

M3 - Article

AN - SCOPUS:84937785180

VL - 64

SP - 929

EP - 941

JO - Linear and Multilinear Algebra

JF - Linear and Multilinear Algebra

SN - 0308-1087

IS - 5

ER -