实对称半正定矩阵的三角(LL^T)分解

The Triangular Decomposition(LL^T) of the Positive Semidefinite Symmetric Real Matrix

设A为n阶实对称半正定矩阵 ,若存在一个对角线上元素全为非负的下三角阵L ,使A =LLT,称为对A的三角分解。本文讨论了实对称半正定矩阵的三角分解的存在性以及这种分解的唯一性的充要条件 。

Let n×n be positive semi definite symmetric real matrix.It is called triangular decomposition of matrix A if A=LL T ,Matrix L is a lower triangular matrix whose elements on diagnal line are noanegative.In this paper,discussed is the existence and a necessary and sufficient condition of the triangular decomposition uniqueness,and then presented is algorithm of the triangular decompsition of the positive semi definite symmetric real matrix.