Infimum of a pair of matrices
type: Item
instance of: scholarly article
title: Infimum of a pair of matrices
zbMATH Open document ID: 0649.15002
DOI: 10.1016/0024-3795(88)90010-9
author: Sujit Kumar Mitra
published in: Linear Algebra and its Applications
publication date: 1988-01-01T00:00:00Z
review text: For a given matrix A, the author denotes by A - a generalized inverse of A, i.e. a matrix G satisfying \(AGA=A\). If rank \(A=rank\) A 2, then the group inverse \(A^{\#}\) of A is the unique solution G of the system of matrix equations \(AGA=A\), \(GAG=G\), \(AG=GA\). In the set of all matrices of fixed dimension, the binary relation \(A\leq B\) whenever A \(-A=A\)-B and AA \(-=BA\)-, is a partial order, called the minus partial order. In the set of all n by n matrices A satisfying rank \(A=rank\) A 2, the binary relation \(A^{\#}<B\) whenever \(A^{\#}A=A^{\#}B\) and \(AA^{\#}=BA^{\#}\), is a partial order, called the sharp order. The author investigates when an infimum of A and B with respect to each order exists. For this, he obtains a criterion for the possibility to extend a given k by m matrix \((k<m)\) to an idempotent m by m matrix, as well as other, similar, results on matrix idempotents.
Mathematics Subject Classification ID: 15A09
Mathematics Subject Classification ID: 15A23
Mathematics Subject Classification ID: 15A24
zbMATH DE Number: 4059587
zbMATH Keywords: generalized inverse
zbMATH Keywords: group inverse
zbMATH Keywords: matrix equations
zbMATH Keywords: minus partial order
zbMATH Keywords: sharp order
zbMATH Keywords: infimum
zbMATH Keywords: matrix idempotents
reviewed by: Mark Kleiner
MaRDI profile type: Publication
full work available at URL: 0024-3795(88)90010-9
OpenAlex ID: W2117968703
cites work: Q3884160
cites work: Lattice properties of the *-order for complex matrices
cites work: On some characterizations of the ''star'' partial ordering for matrices and rank subtractivity
cites work: Q5556523
cites work: The minus partial order and the shorted matrix
cites work: On group inverses and the sharp order
cites work: Shorted matrices - an extended concept and some applications
cites work: The natural partial order on a regular semigroup
cites work: Q5645536
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description: scientific article; zbMATH DE number 4059587