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Author: search.filters.author.Roy, F.Subject: search.filters.subject.Generalized inverses

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    A W-weighted generalization of {1,2,3,1k}-inverse for rectangular matrices
    (Springer Science and Business Media B.V., 2024) Chowdhry, G.; Roy, F.
    This paper presents a novel extension of the {1,2,3,1k}-inverse concept to complex rectangular matrices, denoted as a W-weighted {1,2,3,1k}-inverse, using a complex rectangular matrix W. The study begins by introducing a weighted {1,2,3}-inverse along with its representations and characterizations. The paper establishes criteria for the existence of the proposed inverses based on rank equalities and extends it to weighted inner inverses. The work additionally establishes various representations, properties and characterizations of W-weighted {1,2,3,1k}-inverses, including canonical representations derived through singular value and core-nilpotent decompositions. This, in turn, yields distinctive canonical representations and characterizations of the set A{1,2,3,1k}. Furthermore, it is shown that W-weighted {1,2,3,1k}-inverse is unique if and only if it has index 0 or 1, reducing it to the weighted core inverse. © The Author(s), under exclusive licence to The Forum D’Analystes 2024.
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    Characterizations of {1, 3}-Bohemian inverses of structured matrices
    (University of Nis, 2025) Chowdhry, G.; Stanimirovi?, P.S.; Roy, F.
    This paper presents {1, 3}-Bohemian inverses of a certain type of structured {?1, 0, 1}-matrices, particularly full and well-settled matrices. It begins by characterizing the rank-one Bohemian matrices for the population P = {?1, 0, 1}. Characterizations of the {3} and {1, 3}-Bohemian inverses are presented for arbitrary population over the set {?1, 0, 1}. Furthermore, explicit formulas are provided to enumerate the {1, 3}-Bohemian inverses of these matrices when the population is exactly {?1, 0, 1}. Moreover, corresponding results for {3}-inverses are obtained. © 2025, University of Nis. All rights reserved.