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Keywords:
inverse eigenvalue problem; leading principal submatrices; graph of a matrix; eigenpair
inverse eigenvalue problem; leading principal submatrices; graph of a matrix; eigenpair
Summary:
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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