Hadamard幂下不可约M矩阵最小特征值界的研究

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.

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

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( A  B- 1) of nonnegative matrix A  B- 1; secondly,when every element of A is 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.