非负矩阵Hadam ard积和M-矩阵Fan积的特征值界的估计

周平,李耀堂

(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)

非负矩阵Hadam ard积和M-矩阵Fan积的特征值界的估计

周平1,李耀堂2

(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)

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.

非负矩阵;M-矩阵;Hadamard积;Fan积;谱半径;最小特征值

1 预备知识

2 两个非负矩阵的H adam ard积的谱半径的上界

3 q(A⋆B)的下界

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Estimating of bounds on eigenvalues of the H adam ard p roduct for nonnegative m atrices and the Fan p roduct of M-m atrices

Zhou Ping1,Li Yaotang2

(1.School of M athem atics and Physics,Wenshan University,Wenshan 663000,China; 2.School of M athem atics and Statistics,Yunnan University,Kunm ing 650091,China)

The Hadamard p roduct and the Fan product ofmatrices are im portant prob lem s in thematrices theories.For the Hadam ard product of two nonnegative m atrices A and B,two new upper bounds of the spectral radius are given.For the Fan p roduct of two M-m atrices A and B,two new lower bounds of the smallest eigenvalues are given.The given numerical exam p les show that these estimating formulas im prove several existing resu lts in som e cases,and these bounds are easier to calcu late for they are on ly depending on the entries ofm atrices A and B.

nonnegativematrix,M-matrix,Hadamard product,Fan p roduct,spectral radius, sm allest eigenvalue

O151.21

A

1008-5513(2012)06-0826-08

2011-12-03.

国家自然科学基金(10961027).

周平(1987-),硕士,助教,研究方向:矩阵理论及其应用研究.

李耀堂(1958-),博士,教授,研究方向:数值计算及其应用研究.

2010 M SC:15A 42,15A 69