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Journal of Applied Mathematics
Volume 2014 (2014), Article ID 513513, 7 pages
http://dx.doi.org/10.1155/2014/513513
Research Article

Extremal Inverse Eigenvalue Problem for a Special Kind of Matrices

1School of Sciences, Jiujiang University, Jiujiang 332005, China
2Faculty of Library, Jiujiang University, Jiujiang 332005, China

Received 11 June 2013; Accepted 13 December 2013; Published 5 February 2014

Academic Editor: Hui-Shen Shen

Copyright © 2014 Zhibing Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider the following inverse eigenvalue problem: to construct a special kind of matrix (real symmetric doubly arrow matrix) from the minimal and maximal eigenvalues of all its leading principal submatrices. The necessary and sufficient condition for the solvability of the problem is derived. Our results are constructive and they generate algorithmic procedures to construct such matrices.