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 |
|---|---|
| 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
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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 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
VL - 64
SP - 929
EP - 941
JO - Linear and Multilinear Algebra
JF - Linear and Multilinear Algebra
SN - 0308-1087
IS - 5
ER -