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 ‘’ holds whenever is lesser than 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 is further probed and a general condition for such invariance is obtained for matrices over a commutative ring.
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