A study of the minimum eigenvalue of irreducible M-matrix in connection with the Hadamard power

蒋建新 JJX


利用不可约非负矩阵A的Hadamard幂,矩阵特征值存在域定理,以及非奇异M矩阵B的若干性质,首先给出了不可约非负矩阵A○B-1的谱半径的上界;其次,当A的每个元素都为1时,给出了τ(B)的一些新下界.数值例子说明这些新界一定程度上提高了已有文献中的结果. By using the Hadamard power of irreducible nonnegative matrix A, the existence theorem of the matrix eigenvalues, and some properties of nonsingular M matrix, this paper firstly gives the spectral ρ (AB-1 ) of nonnegative matrix AB-1; secondly, when every element of Ais 1, some new lower bounds of τ (B) are given. Numerical examples illustrate that the results of these new bounds have improved the prior results.


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