分块矩阵及应用

分块矩阵及应用

摘 要

矩阵是1种新的运算对象，我们应该充分注意矩阵运算的1些特殊规律。为了研究问题的需要，适当地对矩阵进行分块，把1个大矩阵看成是由1些小矩阵块为元素组成的，这样可使矩阵的结构看的更清楚。矩阵分块的思想在线性代数证明、应用中是10分有用的。运用矩阵分块的思想，可使解题更简洁，思路更开阔。本文将矩阵分块的方法到

行列式运算、解线性方程组、判断向量线性相关性及有关矩阵秩的证明，特别是找出在2次型化标准形中的应用。

关键词：分块矩阵；线性代数；矩阵的秩；初等矩阵

Block Matrix and Its Application

Abstract

Matrix is a kind of new operation target, and we should pay full attention to the special law in operating the matrix. In order to make the structure of matrix more clearly, when we study this matter, we can divide matrix properly, and regard a big matrix as some small ones, which integrate it. The thought of dividing matrix into blocks is very important in proving and applying the linear algebra. Use the thought of dividing matrix to blocks can help us to solve problems more pithily and think methods more widely. This thesis uses the blocking matrix method into the calculation of determinant, tries to solve the linear equations, Vector judgment linear correlation matrix and the proof of other relative Matrix rank , especially in finding the applications in the secondary-type standards.

Key words: Block matrix；linear algebra；rank of matrix；elementary matrix