非负矩阵Hadamard积和M-矩阵Fan积的特征值界的估计  

Estimating of bounds on eigenvalues of the Hadamard product for nonnegative matrices and the Fan product of M-matrices

作　　者：周平[1] 李耀堂[2] 

机构地区：[1]文山学院数理系,云南文山663000 [2]云南大学数学与统计学院,云南昆明650091

出　　处：《纯粹数学与应用数学》2012年第6期826-833,共8页Pure and Applied Mathematics

基　　金：国家自然科学基金(10961027)

摘　　要：矩阵的Hadamard积和Fan积是矩阵理论研究的重要问题之一.对于两个非负矩阵A和B的Hadamard积,给出了它的谱半径上界的两个新的估计式;同时对于两个非奇异M-矩阵A和B的Fan积,给出了它的最小特征值下界的两个新的估计式;算例表明,所得估计式在某些情况下比现有估计式更为精确,并且这些估计式都只依赖于矩阵A和B的元素,更容易计算.The Hadamard product and the Fan product of matrices are important problems in the matrices theories. For the Hadamard product of two nonnegative matrices .4 and B, two new upper bounds of the spectral radius are given. For the Fan product of two M-matrices A and B, two new lower bounds of the smallest eigenvalues are given. The given numerical examples show that these estimating formulas improve several existing results in some cases, and these bounds are easier to calculate for they are only depending on the entries of matrices A and B.

关 键 词：非负矩阵 M-矩阵 HADAMARD积 Fan积 谱半径 最小特征值 

分 类 号：O151.21[理学—数学]