一类实对称矩阵正定的充分条件

The Sufficient Condition of One Class Rear Symmetric Positive Definite Matrices

如何判断一个实对称矩阵的正定性,尽管有多种方法,但是,当矩阵的阶数n较大时,要判断一个实对称矩阵的正定性,并不是一件容易的事。为此,根据矩阵正定性的主对角线严格占优判别法,讨论了一类未必是主对角线严格占优的实对称矩阵的正定性,给出快速判断这一类实对称矩阵正定的一个充分条件。

In this paper,we discuss the positive definition of one class of real symmetric matrices which is not every entry is strictly main diagonal dominance,then a novel method to determine the matrices are positive definite or is not given with rigorous proves and it is based on the maximal and minimal elements of the determined matrix.