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Journal of Applied Mathematics
Volume 2014, Article ID 535716, 8 pages
Research Article

Inequalities for the Minimum Eigenvalue of Doubly Strictly Diagonally Dominant -Matrices

1School of Mathematical Sciences, Kaili University, Kaili 556011, China
2School of Mathematics and Statistics, Yunnan University, Kunming 650091, China

Received 28 June 2014; Accepted 31 July 2014; Published 17 August 2014

Academic Editor: Shi-Liang Wu

Copyright © 2014 Ming Xu 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.


Let be a doubly strictly diagonally dominant -matrix. Inequalities on upper and lower bounds for the entries of the inverse of are given. And some new inequalities on the lower bound for the minimal eigenvalue of and the corresponding eigenvector are presented to establish an upper bound for the -norm of the solution for the linear differential system , .