Journal Menu

- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents

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

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

#### Linked References

- A. Borobia, “On the nonnegative eigenvalue problem,”
*Linear Algebra and Its Applications*, vol. 223/224, pp. 131–140, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - M. Fang, “A note on the inverse eigenvalue problem for symmetric doubly stochastic matrices,”
*Linear Algebra and Its Applications*, vol. 432, no. 11, pp. 2925–2927, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - S.-G. Hwang and S.-S. Pyo, “The inverse eigenvalue problem for symmetric doubly stochastic matrices,”
*Linear Algebra and Its Applications*, vol. 379, pp. 77–83, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - I. Kaddoura and B. Mourad, “On a conjecture concerning the inverse eigenvalue problem of $4\times 4$ symmetric doubly stochastic matrices,”
*International Mathematical Forum*, vol. 31, no. 3, pp. 1513–1519, 2008. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - T. J. Laffey and E. Meehan, “A characterization of trace zero nonnegative $5\times 5$ matrices,”
*Linear Algebra and Its Applications*, vol. 302/303, pp. 295–302, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - R. Loewy and D. London, “A note on an inverse problem for nonnegative matrices,”
*Linear and Multilinear Algebra*, vol. 6, no. 1, pp. 83–90, 1978. View at Publisher · View at Google Scholar · View at MathSciNet - B. Mourad, “On a spectral property of doubly stochastic matrices and its application to their inverse eigenvalue problem,”
*Linear Algebra and Its Applications*, vol. 436, no. 9, pp. 3400–3412, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - A. M. Nazari and F. Sherafat, “On the inverse eigenvalue problem for nonnegative matrices of order two to five,”
*Linear Algebra and Its Applications*, vol. 436, no. 7, pp. 1771–1790, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - H. Perfect and L. Mirsky, “Spectral properties of doubly-stochastic matrices,”
*Monatshefte für Mathematik*, vol. 69, pp. 35–57, 1965. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - R. Reams, “An inequality for nonnegative matrices and the inverse eigenvalue problem,”
*Linear and Multilinear Algebra*, vol. 41, no. 4, pp. 367–375, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - O. Rojo and R. L. Soto, “Existence and construction of nonnegative matrices with complex spectrum,”
*Linear Algebra and Its Applications*, vol. 368, pp. 53–69, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - J. Torre-Mayo, M. R. Abril-Raymundo, E. Alarcia-Estévez, C. Marijuán, and M. Pisonero, “The nonnegative inverse eigenvalue problem from the coefficients of the characteristic polynomial. EBL digraphs,”
*Linear Algebra and Its Applications*, vol. 426, no. 2-3, pp. 729–773, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - S. Yang and X. Li, “Inverse eigenvalue problems of $4\times 4$ irreducible nonnegative matrices,” in
*Advances in Matrix Theory and Applications. Proceedings of the 8th International Conference on Matrix theory and Applications*, vol. I, World Academic Union, 2008. View at Google Scholar - S. Yang and C. Xu, “Row stochastic inverse eigenvalue problem,”
*Journal of Inequalities and Applications*, vol. 2011, article 24, 5 pages, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - R. A. Horn and C. R. Johnson,
*Matrix Analysis*, Cambridge University Press, Cambridge, UK, 1985. View at MathSciNet