# Inverse eigenvalue problems for centrosymmetric matrices under a central principal submatrix constraint

Volume 17, Issue 4, pp 477-487

Publication Date: 2017-10-14

http://dx.doi.org/10.22436/jmcs.017.04.04

### Authors

Li-Jun Zhao - School of Mathematics and Information Engineering, Taizhou University, Linhai, Zhejiang, 317000, P. R. China
Ru Huang - Department of Mathematics and Computer Science, Emory University, Atlanta, Georgia 30322, USA

### Abstract

This article considers an inverse eigenvalue problem for centrosymmetric matrices under a central principal submatrix constraint and the corresponding optimal approximation problem. We first discuss the specified structure of centrosymmetric matrices and their central principal submatrices. Then we give some necessary and sufficient conditions for the solvability of the inverse eigenvalue problem, and we derive an expression for its general solution. Finally, we obtain an expression for the solution to the corresponding optimal approximation problem.

### Keywords

Centrosymmetric matrix, central principal submatrix, inverse eigenvalue problem, optimal approximation problem

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