The Moore-Penrose inverse of symmetric matrices with nontrivial equitable partitions

Abdullah Alazemi, Milica Anđelić and Dragana Cvetković-Ilić

Applied Mathematics and Computation, 2021, vol. 400, issue C

Abstract: In this paper we consider symmetric matrices that admit nontrivial equitable partitions. We determine some sufficient conditions for the quotient matrix of the Moore-Penrose inverse of the initial matrix to be equal to the Moore-Penrose inverse of its quotient matrix. We also study several particular cases when the computation of the Moore-Penrose inverse can be reduced significantly by establishing the formula for its computation based on the Moore-Penrose inverse of the quotient matrix. Among others we consider the adjacency matrix of a generalized weighted threshold graph.

Keywords: Equitable partitions; Moore-Penrose inverse; Stepwise matrices (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:400:y:2021:i:c:s0096300321000849

DOI: 10.1016/j.amc.2021.126036

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