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

Cahit Köme ()
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Cahit Köme: Nevşehir Hacı Bektaş Veli University

Indian Journal of Pure and Applied Mathematics, 2024, vol. 55, issue 1, 138-152

Abstract: 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 $$(p,q)-$$ ( p , q ) - Pascal matrices of the first and of the second kind. Moreover, we give factorization of the singular conditional matrices via $$(p,q)-$$ ( 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.

Keywords: Moore–Penrose inverse; Pascal matrix; Combinatorial identities; Recurrence sequences (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s13226-022-00352-4

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