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Inverse Eigenvalue Problem for Constructing a Kind of Acyclic Matrices with Two Eigenpairs

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We investigate an inverse eigenvalue problem for constructing a special kind of acyclic matrices. The problem involves the reconstruction of the matrices whose graph is an m-centipede. This is done by using the (2m − 1)st and (2m)th eigenpairs of their leading principal submatrices. To solve this problem, the recurrence relations between leading principal submatrices are used.

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Correspondence to Seyed Abolfazl Shahzadeh Fazeli.

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Zarch, M.B., Fazeli, S.A.S. & Karbassi, S.M. Inverse Eigenvalue Problem for Constructing a Kind of Acyclic Matrices with Two Eigenpairs. Appl Math 65, 89–103 (2020).

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  • inverse eigenvalue problem
  • leading principal submatrices
  • graph of a matrix
  • eigenpair

MSC 2010

  • 65F18
  • 05C50