Abstract
Using a estimate on the Perron root of the nonnegative matrix in terms of paths in the associated directed graph, two new upper bounds for the Hadamard product of matrices are proposed. These bounds improve some existing results and this is shown by numerical examples.
Highlights
Let Mn denote the set of all n × n complex matrices and N denote the set {1, 2, ..., n}
If aij - bij ≥ 0, we say that A ≥ B, and if aij ≥ 0, we say that A is nonnegative
The spectral radius of A is denoted by r(A)
Summary
Let Mn denote the set of all n × n complex matrices and N denote the set {1, 2, ..., n}. Let A = (aij), B = (bij) Î Mn. If aij - bij ≥ 0, we say that A ≥ B, and if aij ≥ 0, we say that A is nonnegative. The spectral radius of A is denoted by r(A). If A is a nonnegative matrix, the Perron-Frobenius theorem guarantees that r(A) Î s(A), where s(A) denotes the spectrum of A
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