Inverse Eigenvalue Problems for Two Special Acyclic Matrices

Debashish Sharma and Mausumi Sen
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Debashish Sharma: Department of Mathematics, Gurucharan College, College Road, Silchar 788004, India
Mausumi Sen: Department of Mathematics, National Institute of Technology Silchar, Silchar 788010, India

Mathematics, 2016, vol. 4, issue 1, 1-11

Abstract: In this paper, we study two inverse eigenvalue problems (IEPs) of constructing two special acyclic matrices. The first problem involves the reconstruction of matrices whose graph is a path, from given information on one eigenvector of the required matrix and one eigenvalue of each of its leading principal submatrices. The second problem involves reconstruction of matrices whose graph is a broom, the eigen data being the maximum and minimum eigenvalues of each of the leading principal submatrices of the required matrix. In order to solve the problems, we use the recurrence relations among leading principal minors and the property of simplicity of the extremal eigenvalues of acyclic matrices.

Keywords: inverse eigenvalue problem; leading principal minors; graph of a matrix (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2016
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