Authors
Citation
Yz. Song, On an inequality for the Hadamard product of an M-matrix and its inverse, LIN ALG APP, 305(1-3), 2000, pp. 99-105
Citations number
6
Categorie Soggetti
Mathematics
Journal title
LINEAR ALGEBRA AND ITS APPLICATIONS
ISSN journal
00243795
→ ACNP
Volume
305
Issue
1-3
Year of publication
2000
Pages
99 - 105
Database
ISI
SICI code
0024-3795(20000115)305:1-3<99:OAIFTH>2.0.ZU;2-6
Abstract
When A is an element of R-nxn is an M-matrix we prove the following inequal
ity:
q(A o A(-1)){= 1 for n=2, > 2/n for n > 2,
where A o B is the Hadamard product of two matrices A and B, q(B) = [p(B-1)
](-1) and p(C) denotes the Perron eigenvalue of a nonnegative matrix C. Thi
s also gives a positive answer to the conjecture posed by Fiedler and Markh
am. (C) 2000 Elsevier Science Inc. All rights reserved.