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<p>We study the inverse problem for singular, irreducible, symmetric <i>M</i>-matrices that consists in characterizing those for which the group inverse is again an <i>M</i>-matrix. We solve the problem for a structured class of such matrices arising from star graphs by employing both matrix-theoretic tools and potential theory on networks. Our approach yields explicit criteria for the <i>M</i>-property of the group inverse in terms of conductances and Doob potentials, and provides a constructive procedure to obtain such families of matrices with the desired property.</p>

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The M-matrix group inverse problem for star networks

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月3日

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  • Á. Carmona,
  • A. M. Encinas,
  • S. Patra,
  • K. C. Sivakumar

摘要

We study the inverse problem for singular, irreducible, symmetric M-matrices that consists in characterizing those for which the group inverse is again an M-matrix. We solve the problem for a structured class of such matrices arising from star graphs by employing both matrix-theoretic tools and potential theory on networks. Our approach yields explicit criteria for the M-property of the group inverse in terms of conductances and Doob potentials, and provides a constructive procedure to obtain such families of matrices with the desired property.