Applications of Mathematics, Vol. 65, No. 1, pp. 89-103, 2020


Inverse eigenvalue problem for constructing a kind of acyclic matrices with two eigenpairs

Maryam Babaei Zarch, Seyed Abolfazl Shahzadeh Fazeli, Seyed Mehdi Karbassi

Received April 22, 2019.   Published online January 20, 2020.

Abstract:  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.
Keywords:  inverse eigenvalue problem; leading principal submatrices; graph of a matrix; eigenpair
Classification MSC:  65F18, 05C50


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Affiliations:   Maryam Babaei Zarch, Seyed Abolfazl Shahzadeh Fazeli (corresponding author), Seyed Mehdi Karbassi, Yazd University, Safayieh, P. O. Box: 98195-741, Yazd, Yazd Province, Iran, e-mail: maryam.babaei@stu.yazd.ac.ir, fazeli@yazd.ac.ir, smkarbassi@yazd.ac.ir


 
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