摘要矩阵的初等变换在数学科学领域里当作一个演算工具之一,高等代数中相关的计算问题由矩阵的初等变换来解决.不仅用来求解线性方程组,还有求矩阵的逆矩阵,计算行列式,求矩阵的秩,判断向量间的线性关系(判定向量组的线性相关性,向量组的秩与极大线性无关组的关系的研究,求向量在一组基下的坐标,判定两个向量组之间的线性关系等).分别求出两个向量组生成的子空间的和与交的维数与基等. 在此论文中矩阵的初等变换与高等代数的密切关系进行了进一步的探究,深化,发散思维,从多的角度揭示了初等变换在高等代数内在关联并举例论证.52852
毕业论文关键词 :初等变换 秩 极大线性无关组 逆矩阵
The Application of the Elementary transformation of matrix in higher algebra
Abstract
Elementary transformation of matrix in the mathematical sciences as a calculation tool, one of the advanced algebra in the relevant calculation by the elementary transformation of matrix to solve the problem. Not only is used to solve the linear system of equations, and calculate the inverse matrix, the ma trix calculation of determinant, matrix rank, to judge linear relationship between vector (linear correlation decision vectors, the vector group rank of a study of the relationship with maximum linearly independent group, the coordinates of the vector in a set of base, and judging what kind of linear relationship between two vectors, etc.). The calculated respectively two vectors generated by the dimension of sum and intersection of subspace ,and the base and so on. In this paper the elementary transformation of matrix and the advanced algebra has carried on the further study of close relations, deepening, pergent thinking, reveals the elementary transformation from the perspective of more interconnectedness and illustrate in higher algebra.
Key words: Elementary transformation Rank Maximum impertinent groups Inverse matrix
目录
摘要--Ⅰ
Abstract-Ⅱ
目录--Ⅲ
1绪论 ---1
1·1矩阵的初等变换与初等矩阵---1
2 行列式的计算---2
3 用初等变换求线性方程组的解2
4 求矩阵的秩--3
5 求矩阵的逆矩阵3
6 判断向量组的线性相关性---4
6.1向量组的秩与极大线性无关组--5
6.2 向量在一组基下的坐标---6
7 子空间的基与维数-7
7·1 子空间的和--8
8 结束语-9
参考文献-9
致谢---10
1绪论
矩阵的初等变换是在矩阵领域中体现了多种应用.代数中必不可少的重要部分之一的矩阵理论在研究其它的学科中也有很大的作用.矩阵的初等变作为高等代数中的一个基本概念,在解线性方程组里应用最广泛.它已成为高等代数研究问题中必不可少的工具,几乎贯通于整个高等代数,初等行变换使研究矩阵与行列式中起着重要作用,提供了一个广大的空间.用初等变换研究矩阵,矩阵的逆矩阵,线性方程组的求解的问题,向量组的线性相关性,向量组的秩与极大线性无关组,在一组基下的坐标,二次型等等.下面就用例题来探索矩阵初等变换在高等代数中的几个应用.
1·1矩阵的初等变换与初等矩阵
(1) 一个矩阵称为矩阵的初等变换,如果有一下几种变换[1]:
i. 交换矩阵的两行(列);
ii. 以一个非零数 乘矩阵的某行(列);
iii. 矩阵的某行(列)加上另一行(列)的 倍;
(2)