矩阵的初等变换及应用

在矩阵的一些应用中,我们经常会遇到一些比较复杂的问题,在这种情况下,我们往往会采用矩阵的初等变换把问题简化.本文根据矩阵初等变换的有关知识,给出了矩阵初等变换在求逆矩阵,求齐次线性方程组的基础解系,化二次型为标准形,求从一组基到另一组基的过渡矩阵,解矩阵方程,求向量组的秩和极大线性无关组,以及矩阵秩的证明等方面的应用.通过运用矩阵的初等变换,可以使高等代数中的有关计算问题变得简单.
关键词 矩阵 初等矩阵 初等变换 矩阵的秩
   The Elementary Transformation of Matrices and Its Applications
      Student Majoring in Mathematics and Applied Mathematics   Wang Yali
    
Abstract  In some applications of the matrix, we often encounter some of the more complex issues, in this case, we often use the elementary transformation of matrix to simplify the problem. In this paper, according to the relevant knowledge of elementary transformation of matrix, gives the elementary transformation of matrix in the inverse matrix, based on homogeneous solution system of linear equations, the two type is a standard type, and the transition matrix from one group to another group of medium, solution of matrix equation, independent set of vectors rank and maximal linear ,applications as as the rank of a matrix by elementary transformation. By using matrix, can make the problem of calculation of higher algebra becomes simple.
Key words  matrix  elementary matrix  elementary transformation  matrix rank of 

引言 矩阵的初等变换是高等代数中的一个重要内容,是矩阵中十分重要的运算,是线性代数的核心,是高等代数中解决问题的一个重要工具.它在求逆矩阵,求解矩阵方程,化二次型为标准形,求向量组的秩和极大线性无关组,还有分块矩阵的初等变换在行列式计算中的应用,矩阵秩的相关证明以及矩阵的理论探讨中都有着十分重要的意义.  

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