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

Author

Listed:
  • Alazemi, Abdullah
  • Anđelić, Milica
  • Cvetković-Ilić, Dragana

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.

Suggested Citation

  • Alazemi, Abdullah & Anđelić, Milica & Cvetković-Ilić, Dragana, 2021. "The Moore-Penrose inverse of symmetric matrices with nontrivial equitable partitions," Applied Mathematics and Computation, Elsevier, vol. 400(C).
    • Handle: RePEc:eee:apmaco:v:400:y:2021:i:c:s0096300321000849
    DOI: 10.1016/j.amc.2021.126036
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    References listed on IDEAS

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    1. Haemers, W.H., 1995. "Interlacing eigenvalues and graphs," Other publications TiSEM 35c08207-2c5c-4387-aaf5-2, Tilburg University, School of Economics and Management.
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