利用矩阵分析二次型对角化

Analysis on the Diagonalization of Quadratic form with Matrix

二次型化标准形常采用配方法,而二次型化标准形等价于它的矩阵合同对角化,文中利用初等矩阵和初等变换之间的关系。从矩阵的角度分析了二次型化标准形中配方法的实质,实际上就是将二次型的矩阵中对角线上某个非零元素所在的行和列化成零。

Method of completing square is often used when transforming a quadratic form into a normal one, whose process is equivalent to making the relevant matrix contract diagonal. This paper analyzes the essence of method of completing suqare with matrix, utilizing the relationship between the elementary matrix and the elementary transformation. In fact, this method can be seen as a process in which the line and the row in the diagonal where some non -vanishing element lies are transformed into zero.