On an inequality for the Hadamard product of an M-matrix and its inverse

✍ Scribed by Yongzhong Song

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 61 KB
• Volume: 305
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/s0024-3795(99)00224-4

✦ Synopsis

When A ∈ R n×n is an M-matrix we prove the following inequality:

where A • 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. This also gives a positive answer to the conjecture posed by Fiedler and Markham.