矩阵的斜初等变换及其应用

The Oblique Elementary Operation of Matrix and Its Application

提出了矩阵的斜初等变换的概念,并给出了矩阵的斜初等变换下的标准形,然后建立了用矩阵的斜初等变换求多项式最大公因式的新方法.最后指出,用矩阵的斜初等变换可方便地求满足u(x)f(x)+v(x)g(x)=d(x)的u(x)和v(x).

In this paper. We advance the concepts of oblique elementary operation of matrix,and proved a standard form under the oblique elementary operation. Then establish a new method of extracting greatest common divisor of polynomial. Finally,finding out u(x) and v(x) which meets u(x)f (x)+v(x)g(x)=d(x) is convenient with the use of oblique elementary operation of matrix.