Reverse Order Law for Generalized Inverses with Indefinite Hermitian Weights
K. Kamaraj, P. Sam Johnson, Athira Satheesh
TL;DR
This paper investigates the conditions under which the reverse order law for Moore-Penrose inverses holds in indefinite inner product spaces, providing new rank formulas and addressing an open problem.
Contribution
It establishes necessary and sufficient conditions for the reverse order law in IIPS and introduces rank equivalence formulas specific to this setting.
Findings
Conditions for reverse order law in IIPS derived
Rank formulas for Moore-Penrose inverse in IIPS provided
Open problem related to indefinite Hermitian weights discussed
Abstract
In this paper, necessary and sufficient conditions are given for the existence of Moore-Penrose inverse of a product of two matrices in an indefinite inner product space (IIPS) in which reverse order law holds good. Rank equivalence formulas with respect to IIPS are provided and an open problem is given at the end.
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Taxonomy
TopicsMatrix Theory and Algorithms · Advanced Optimization Algorithms Research · Advanced Topics in Algebra