利用矩阵分解法判别矩阵的正定性

Using Decomposition Method of Matrix to Discriminate Positive Quality of Matrix

讨论Euclid空间中n阶实对称矩阵A是否正定,一直是矩阵理论中的重要问题。本文一改传统方法,从矩阵分解入手,逐步推导出一种新颖的判定方法,并给出将n阶实对称矩阵A分解为特殊三角矩阵与对角矩阵乘积的具体计算公式。

In the discussion of Euclid space, whether the n order real symmetric matrix A is positive remains an important question in matrix theory. By changing the traditional method and starting with the matrix decomposition, we have made out a new method of judgment step by step and a concrete computing formula of decomposing the n real symmetric matrix A into special triangle matrix and diagonal matrix.