正定矩阵及其应用

Positive Definite Matrix and Its Application

正定矩阵是矩阵理论中非常重要的内容,可以有效地解决代数问题和分析问题.本文结合二次型和正定矩阵的关系,给出了正定矩阵的性质,通过例题阐述了判定矩阵为正定矩阵的常用方法,总结了正定矩阵在分析问题中的若干应用。

Positive definite matrix plays a very important role in matrix theory and can be used to solve a lot of algebraic and analytic problems. Based on the relationship between positive definite matrix and quadratic form, this paper gives the necessary and sufficiency conditions of positive definite matrix. Two methods of the decision of positive definite matrix are given and illustrated by examples. Applications of positive definite matrix in analytic problems are also summarized.