摘要
本文研究M-矩阵的行列式性质。我们首先证明任一M-矩阵都满足Hadamard不等式和Fischer不等式,并讨论这两个不等式中成立等式的充要条件。其次我们给出关于一个M-矩阵和一个三对角线振荡矩阵的Hadamard积的行列式的一个有趣的不等式。最后证明关于n阶M-矩阵各k阶主子式乘积(k=1,…,n)的—个不等式,这个不等式可视为Hadamard不等式的一种推广。
In this paper, we investigate the properties of the determinant of any M-matirix. We prove that any M-matrix satisfies the Hadamrd inequality and the Fischer inequality to hold in cach of these two inequalities. We give an interesting inequality for the determinant of the Hadamard produet of an M-matrix and a tridiagonal oscillatory matrix and for the products of all the k×k principal minors, k=1,…, n of an M-matrix of order n, cstablish, an inequality which, is a kind of generalization of Hadamard inequality.
出处
《工程数学学报》
CSCD
1992年第4期76-84,共9页
Chinese Journal of Engineering Mathematics
