矩阵Hadamard积与Fan积的特征值新界

New Bounds for Eigenvalues of Hadamard Product and Fan Product of Matrices

非负矩阵和M矩阵是矩阵论中两类重要的矩阵.矩阵特征值的研究是如今的重要问题.利用Brauer定理和Gerschgorin定理给出了非负矩阵Hadamard积和非奇异M矩阵Fan积的特征值新界.所有的新结果只依赖相关矩阵的元素,其计算简单容易.将所给定理的优越性进行了理论上的比较.通过数值例子验证所得结果改进了其他文献中的相关结果.

Nonnegative matrix and M-matrix are two important matrices in matrix theory.It is important nowadays to study matrix eigenvalue.New bounds on eigenvalues for the Hadamard product of nonnegative matrices and the Fan product of nonsingular M-matrices are given by using Brauer theorem and Gerschgorin theorem.All new results depend only on the elements of the correlation matrices and are easy to calculate.The advantages of the given theorem are compared in theory.Numerical examples show that the results improve the result of the results in the other literatures.