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

โœ Scribed by Guanghui Cheng, Qin Tan, Zhuande Wang

Book ID
120732823
Publisher
Hindawi Publishing Corporation
Year
2013
Tongue
English
Weight
143 KB
Volume
2013
Category
Article
ISSN
1025-5834

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๐Ÿ“œ SIMILAR VOLUMES

On an inequality for the Hadamard produc
On an inequality for the Hadamard product of an M-matrix and its inverse
โœ Yongzhong Song ๐Ÿ“‚ Article ๐Ÿ“… 2000 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 61 KB

When A โˆˆ R nร—n is an M-matrix we prove the following inequality: where A โ€ข 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.