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Some inequalities for the minimum eigenvalue of the Hadamard product of an M-matrix and its inverse

Guanghui Cheng*, Qin Tan and Zhuande Wang

Author Affiliations

School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan, 611731, P.R. China

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Journal of Inequalities and Applications 2013, 2013:65  doi:10.1186/1029-242X-2013-65

Published: 21 February 2013

Abstract

In this paper, some new inequalities for the minimum eigenvalue of the Hadamard product of an M-matrix and its inverse are given. These inequalities are sharper than the well-known results. A simple example is shown.

AMS Subject Classification: 15A18, 15A42.

Keywords:
Hadamard product; M-matrix; inverse M-matrix; strictly diagonally dominant matrix; eigenvalue