矩阵的初等变换及应用.docVIP

目 录 摘要...............................................................1 1 矩阵的初等变换...................................................2 1.1矩阵的初等变换......................................2 1.2阶梯矩阵与最简化阶梯矩阵............................3 1.3初等矩阵与初等变换关系..............................4 2 矩阵初等变换的应用.......................................5 2.1齐次线性方程组的解空间..............................5 2.2求解线性方程组......................................6 2.3求可逆矩阵..........................................8 2.4求极大线性无关组....................................9 2.5对称矩阵A的对角化..................................10 参考文献...............................................13 致谢...................................................13 矩阵的初等变换及应用 【摘要】本文主要讲矩阵的初等变换与初等变换的广泛应用，初等变换包括行变换与列变换，主要以行变换为例，通过行变换将一个矩阵化成与之等价的简化阶梯矩阵用于求其次线性方程组的解空间，解方程组，判断矩阵是否可逆，若可逆求逆矩阵以及用初等变换法在中求极大线性无关组和对称矩阵A的对角化等等。 【关键词】 矩阵 初等变换 应用 【ABSTRACT】 this paper about the elementary transformation matrix with primary transpositions is widely, elementary transformation and transform matrix included, mainly transformation of line as an example, through the transformation of line into A matrix and the equivalent for the next step matrix simplify the solution of linear equations, the solution of equations, the space is reversible, if the judgement matrix inverse matrix and reversible elemtntary transformation in the maximal linear irrelevant for bisymmetric matrices and A group of diagonalization etc. 【KEY-WORDS】