Research ArticleNo Access

On the semiring of generalized inverses of a matrix

P. H. Sathi

Department of Mathematics, CUSAT, Kochi, Kerala, India

E-mail Address: sathiph1975@cusat.ac.in

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and

P. G. Romeo

https://orcid.org/0000-0001-9539-7810

Department of Mathematics, CUSAT, Kochi, Kerala, India

E-mail Address: romeopg@cusat.ac.in

Corresponding author.

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https://doi.org/10.1142/S1793557124500931Cited by:0 (Source: Crossref)

Abstract

In this paper, we consider the set of all generalized inverses of an $m \times n$ matrix $A$ , denoted by $A {1}$ and define two binary operations, ⊕ and ⋆ with some properties which offer the structure of a semi ring to $A {1}$ . The compatibility of some partial orders like Sussman’s order, Conrad’s order, etc. is also checked which make it an ordered matrix semiring.

Communicated by A. R. Rajan

Keywords:

AMSC: 06F05, 15A09, 06A06

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