Browsing by Author "Roy, F."

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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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    Additive Properties of the generalized and pseudo n-strong Drazin Inverse in Banach Algebras
    (Indian National Science Academy, 2025) Biswas, R.; Roy, F.
    In this paper, we establish some necessary and sufficient conditions for generalized n-strong Drazin invertibility (gns-invertibility) and pseudo n-strong Drazin invertibility (pns-invertibility) of an element in a Banach algebra for n?N. Subsequently, these results are utilized to prove some additive properties of gns (pns)-Drazin inverse. This process produces a generalization of some recent results of H Chen, M Sheibani (Linear and Multilinear Algebra 70.1 (2022): 53-65) for gns and pns-Drazin inverse. © The Indian National Science Academy 2025.
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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.
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    Comprehensive classification of the algebra generated by two idempotent matrices
    (Elsevier Inc., 2025) Biswas, R.; Roy, F.
    For two idempotent matrix P,Q?Cn×n, let alg(In,P,Q) denote the smallest subalgebra of Cn×n that contains P,Q and the identity matrix In. This paper provides a complete classification of alg(In,P,Q) without imposing any restrictions on P and Q. As a result of this classification, the issue of group invertibility within alg(In,P,Q) is fully resolved. © 2024 Elsevier Inc.
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    Computing the Moore-Penrose inverse using its error bounds
    (2020) Stanimirovi?, P.S.; Roy, F.; Gupta, D.K.; Srivastava, S.
    A new iterative scheme for the computation of the Moore-Penrose generalized inverse of an arbitrary rectangular or singular complex matrix is proposed. The method uses appropriate error bounds and is applicable without restrictions on the rank of the matrix. But, it requires that the rank of the matrix is known in advance or computed beforehand. The method computes a sequence of monotonic inclusion interval matrices which contain the Moore-Penrose generalized inverse and converge to it. Successive interval matrices are constructed by using previous approximations generated from the hyperpower iterative method of an arbitrary order and appropriate error bounds of the Moore-Penrose inverse. A convergence theorem of the introduced method is established. Numerical examples involving randomly generated matrices are presented to demonstrate the efficacy of the proposed approach. The main property of our method is that the successive interval matrices are not defined using principles of interval arithmetic, but using accurately defined error bounds of the Moore-Penrose inverse. 2019 Elsevier Inc.
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    Computing the Moore-Penrose inverse using its error bounds
    (Elsevier Inc. usjcs@elsevier.com, 2020) Stanimirovi?, P.S.; Roy, F.; Gupta, D.K.; Srivastava, S.
    A new iterative scheme for the computation of the Moore-Penrose generalized inverse of an arbitrary rectangular or singular complex matrix is proposed. The method uses appropriate error bounds and is applicable without restrictions on the rank of the matrix. But, it requires that the rank of the matrix is known in advance or computed beforehand. The method computes a sequence of monotonic inclusion interval matrices which contain the Moore-Penrose generalized inverse and converge to it. Successive interval matrices are constructed by using previous approximations generated from the hyperpower iterative method of an arbitrary order and appropriate error bounds of the Moore-Penrose inverse. A convergence theorem of the introduced method is established. Numerical examples involving randomly generated matrices are presented to demonstrate the efficacy of the proposed approach. The main property of our method is that the successive interval matrices are not defined using principles of interval arithmetic, but using accurately defined error bounds of the Moore-Penrose inverse. © 2019 Elsevier Inc.
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    Drazin and group invertibility in algebras spanned by two idempotents
    (Elsevier Inc., 2024) Biswas, R.; Roy, F.
    For two given idempotents p and q from an associative algebra A, in this paper, we offer a comprehensive classification of algebras spanned by the idempotents p and q. This classification is based on the condition that p and q are not tightly coupled and satisfy (pq)m−1=(pq)m but (pq)m−2p≠(pq)m−1p for some m(≥2)∈N. Subsequently, we categorize all the group invertible elements and establish an upper bound for the Drazin index of any elements in these algebras spanned by p,q. Moreover, we formulate a new representation for the Drazin inverse of αp+q under two different assumptions, (pq)m−1=(pq)m and λ(pq)m−1=(pq)m, where α is a non-zero and λ is a non-unit real or complex number. © 2024 Elsevier Inc.
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    Equivalency of Drazin and g-Drazin invertibility of elements in a Banach algebra
    (Indian National Science Academy, 2025) Biswas, R.; Roy, F.
    Consider a complex unital Banach algebra A. For x1,x2,x3?A, in this paper, we establish that under certain assumptions on x1,x2,x3, Drazin (resp. g-Drazin) invertibility of any three elements among x1,x2,x3 and x1+x2+x3(orx1x2+x1x3+x2x3) ensure the Drazin (resp. g-Drazin) invertibility of the remaining one. As a consequence for two idempotents p,q?A, this result indicates the equivalence between Drazin (resp. g-Drazin) invertibility of (Formula presented.) and (Formula presented.) where ?1,?i?C for i=1,2,?,m, with ?1?1?0; which extend the work of Barraa and Benabdi [1]. Furthermore, for x1,x2, we establish that the Drazin (resp. g-Drazin) invertibility of any two elements among x1,x2 and x1+x2 indicates the Drazin (resp. g-Drazin) invertibility of the remaining one, provided that x1x2=?(x1+x2) for some ??C. Additionally, if it exists, we furnish a new formula to represent the Drazin (resp. g-Drazin) inverse of any element among x1,x2 and x1+x2, by using the other two elements and their Drazin (resp. g-Drazin) inverse. © The Indian National Science Academy 2025.
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    Generalized Core-EP Inverse: Representational and Computational Aspects
    (Indian National Science Academy, 2025) Chowdhry, G.; Roy, F.
    This study obtains several representations and properties of the generalized core-EP inverse (GCEP inverse). A novel canonical representation of the generalized core-EP inverse is obtained using the singular value decomposition (SVD). To accomplish this, a canonical representation of the AT,S(2) is also obtained. Further, utilizing the full-rank decomposition of AT,S(2), some full-rank representations of the GCEP inverse are obtained, which in turn gives some new integral representations of the GCEP inverse. Additionally, algorithms and numerical examples are given using the representations obtained. Algorithms are implemented in Matlab R2024a, and it concluded that our algorithms are reliable and give more accurate results than the existing one in [1]. © The Indian National Science Academy 2025.
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    ON THE ESTIMATION OF q–NUMERICAL RADIUS OF HILBERT SPACE OPERATORS
    (Element D.O.O., 2024) Patra, A.; Roy, F.
    The objective of this article is to estimate the q-numerical radius of bounded linear operators on complex Hilbert spaces. One of our main results states that for a bounded linear operator T in a Hilbert space H and q ∈ [0,1], the relation (Formula Presented) holds where w(T), wq (T) are the numerical radius and q-numerical radius of T respectively. Several refined new upper bounds follow from this result. Finally, the q-numerical radius of 2 × 2 operator matrices is explored and several new results are established. © 2024, Element D.O.O.. All rights reserved.