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On the inverse eigenvalue problem for a special kind of acyclic matrices

Mohammad Heydari;  Seyed Abolfazl Shahzadeh Fazeli;  Seyed Mehdi Karbassi — 2019

Applications of Mathematics

We study an inverse eigenvalue problem (IEP) of reconstructing a special kind of symmetric acyclic matrices whose graph is a generalized star graph. The problem involves the reconstruction of a matrix by the minimum and maximum eigenvalues of each of its leading principal submatrices. To solve the problem, we use the recurrence relation of characteristic polynomials among leading principal minors. The necessary and sufficient conditions for the solvability of the problem are derived. Finally, a...

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

Maryam Babaei Zarch;  Seyed Abolfazl Shahzadeh Fazeli;  Seyed Mehdi Karbassi — 2020

Applications of Mathematics

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 ( 2 m - 1 ) st and ( 2 m ) th eigenpairs of their leading principal submatrices. To solve this problem, the recurrence relations between leading principal submatrices are used.

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