F-矩阵的性质与Hadamard不等式的注记

The properties of the F-matrices and the notes about the Hadamard inequality

通过对正定矩阵、M-矩阵、逆M-矩阵的研究,使用Fisher不等式给出了F-矩阵的定义,并研究了F-矩阵及相关矩阵类的性质,得到的主要结果是:F-矩阵Schur补是F-矩阵;F-矩阵与逆F-矩阵Hadamard不等式等号成立的矩阵结构,以及F-矩阵与逆F-矩阵的一个组合性质.

By the study of definite matrix, M - matrix and inverse M - matrix, F - matrix define is given. In this paper, we investigate the properties of the F - matrix, and prove the following resuhs：Schur comple- ment of F - matrix axe F - matri. We also gain the matrix structures about M - matrix and inverse M - matrix Hadamard inequality when det A=n∏i=1aǖ