“关于正定矩阵判别定理的改进”的一个注记

A Note on "Improvement of Discrimination on the Positive Definite Matrix"

[1]文中介绍利用矩阵的初等保号变换,根据其保号等价矩阵的主对角线元素的符号直接判别矩阵的正定性。本文指出其方法及定理是不够严谨的,指出其错误的原因并给出建议。

The reference introduced sign - reserving transformation , and directly judged the positive definiteness of the matrix by the sign of main diagonal elements of the sign reserving equivalent triangular matrix . This paper shows that the method is not accurate , and gives the causes leading to the mistake as well as advices.