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

摘要

Let A and B be nonsingular M-matrices. Some new lower bounds on the minimum eigenvalue q ( A ° B ? 1 ) for the Hadamard product of A and B ? 1 are given. These bounds improve the corresponding results of Chen (Linear Algebra Appl. 378:159-166, 2004) and Huang (Linear Algebra Appl. 428:1551-1559, 2008) and generalize the corresponding result of Xiang (Linear Algebra Appl. 367:17-27, 2003). MSC:15A06, 15A15, 15A48.