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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 902383, 10 pages
http://dx.doi.org/10.1155/2014/902383
Research Article

On the Inverse Eigenvalue Problem for Irreducible Doubly Stochastic Matrices of Small Orders

1Key Laboratory of Intelligent Computing & Signal Processing, Ministry of Education, Anhui University, Hefei, Anhui 230039, China
2Department of Applied Mathematics, Suzhou University of Science and Technology, Suzhou, Jiangsu 215009, China
3School of Mathematical Sciences, Anhui University, Hefei, Anhui 230039, China

Received 28 July 2013; Accepted 17 January 2014; Published 4 March 2014

Academic Editor: Shusen Ding

Copyright © 2014 Quanbing Zhang 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

The inverse eigenvalue problem is a classical and difficult problem in matrix theory. In the case of real spectrum, we first present some sufficient conditions of a real r-tuple (for ; 3; 4; 5) to be realized by a symmetric stochastic matrix. Part of these conditions is also extended to the complex case in the case of complex spectrum where the realization matrix may not necessarily be symmetry. The main approach throughout the paper in our discussion is the specific construction of realization matrices and the recursion when the targeted r-tuple is updated to a -tuple.