On the semiring of generalized inverses of a matrix

In this paper, we consider the set of all generalized inverses of an [Formula: see text] matrix [Formula: see text], denoted by [Formula: see text] and define two binary operations, ⊕ and ⋆ with some properties which offer the structure of a semi ring to [Formula: see text]. The compatibility of some partial orders like Sussman’s order, Conrad’s order, etc. is also checked which make it an ordered matrix semiring.

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Publication Details

Journal
Asian-European Journal of Mathematics
Published
2024-09-05
DOI
https://doi.org/10.1142/s1793557124500931
Primary Topic
Matrix Theory and Algorithms
Type
article
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article

On the semiring of generalized inverses of a matrix

P. G. Romeo, P. H. Sathi
Asian-European Journal of Mathematics
Matrix Theory and Algorithms
article

On the semiring of generalized inverses of a matrix

P. G. Romeo, P. H. Sathi
article en

Abstract

In this paper, we consider the set of all generalized inverses of an [Formula: see text] matrix [Formula: see text], denoted by [Formula: see text] and define two binary operations, ⊕ and ⋆ with some properties which offer the structure of a semi ring to [Formula: see text]. The compatibility of some partial orders like Sussman’s order, Conrad’s order, etc. is also checked which make it an ordered matrix semiring.

Asian-European Journal of MathematicsVol. 18(01)
Cochin University of Science and Technology (IN)
Openalex Percentile: Top 82%
Matrix Theory and Algorithms
DOISourceOpenAlex
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On the semiring of generalized inverses of a matrix — P. G. Romeo, P. H. Sathi · Asian-European Journal of Mathematics (2024) | TGRS Research Map | TGRS