Minus partial order on regular matrices

Manjunatha Prasad Karantha, Mohana, P. Divya Shenoy

Research output: Contribution to journalArticle

1 Citation (Scopus)

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 languageEnglish
Pages (from-to)929-941
Number of pages13
JournalLinear and Multilinear Algebra
Volume64
Issue number5
DOIs
Publication statusPublished - 03-05-2016

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Partial Order
Commutative Ring
Invariance
Order Relation
Class
Theorem

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Cite this

Karantha, Manjunatha Prasad ; Mohana ; Shenoy, P. Divya. / Minus partial order on regular matrices. In: Linear and Multilinear Algebra. 2016 ; Vol. 64, No. 5. pp. 929-941.
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Minus partial order on regular matrices. / Karantha, Manjunatha Prasad; Mohana; Shenoy, P. Divya.

In: Linear and Multilinear Algebra, Vol. 64, No. 5, 03.05.2016, p. 929-941.

Research output: Contribution to journalArticle

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