矩阵的三角分解及其应用研究  

Matrix's triangular decomposition and its application

作　　者：沈忱[1] 

机构地区：[1]长江大学信息与数学学院,湖北荆州434023

出　　处：《湖南农机（学术版）》2010年第3期94-97,共4页Hunnan Agricultural Machinery

摘　　要：矩阵的三角分解(LU分解)是矩阵分解中最简单、最基础的一种。本文主要对矩阵的三角分解理论分析作了比较全面的统述,它包括矩阵三角分解存在唯一性的充要条件、存在性的充要条件等.并介绍了三类特殊矩阵的三角分解,且对矩阵三角分解的计算及应用作了较详细的论述.最后,本文特别例举了比较有意思的简单多项式矩阵的分解。Matrix＇s triangular decomposition（LU decomposition） is the simplest and most basic kind of decomposition in matrix decomposition.In this paper,the theoretical analysis of matrix＇s triangular decomposition is mainly discussed,including such as the necessary and sufficient condition of uniqueness of existence in matrix＇s triangular decomposition and so on.And three special kind of triangular decomposition is introduced.In addition,the calculation of matrix＇ s triangular decomposition and the application on matrix＇ s triangular decomposition are detailedly discussed.At last a meaningful decomposition of simple polynomial matrix is drawn as a special example in this paper.

关 键 词：上(下)三角矩阵 三角分解 满秩矩阵 逆序主子行列式 

分 类 号：O151.21[理学—数学]