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Moore−Penrose inverse of the singular conditional matrices and its applications

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Abstract

The purpose of this paper is to provide a broad results on the investigation of the Moore–Penrose inverses of singular conditional matrices formed by generalized conditional sequences. By using some analytical techniques, we obtain explicit Moore–Penrose inverse of the singular conditional matrices whose elements are the generalized conditional sequences. We investigate the correlations between singular conditional matrices and the \((p,q)-\)Pascal matrices of the first and of the second kind. Moreover, we give factorization of the singular conditional matrices via \((p,q)-\)Pascal matrices. We derive several combinatorial identities and provide more generalized results. Finally, we provide better numerical results compared to MATHEMATICA’s PseudoInverse function which uses Singular Value Decomposition (SVD) algorithm.

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Authors and Affiliations

  1. Department of Mathematics, Nevşehir Hacı Bektaş Veli University, Nevşehir, 50300, Turkey

    Cahit Köme

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  1. Cahit Köme
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Correspondence to Cahit Köme.

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Communicated by B. Sury.

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Köme, C. Moore−Penrose inverse of the singular conditional matrices and its applications. Indian J Pure Appl Math 55, 138–152 (2024). https://doi.org/10.1007/s13226-022-00352-4

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  • DOI: https://doi.org/10.1007/s13226-022-00352-4

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