主理想整环上的线性方程组的通解

On the General Solution of a System of Linear Equations over Principal Ideal Domain

将文[1]中整数环上的线性方程组问题推广到主理想整环上,利用主理想整环上的矩阵的初等变换及等价标准形导出了主理想整环上的线性方程组有解的一个充分必要条件和求解方法.最后,通过实例说明了算法.

This paper extends the result in[1] and studies the solution of a system of linear equations over principal ideal domain. By using the elementary transformation of a matrix over principal ideal domain, the necessary and sufficient condition for existence of a solution and a method to find the solutions are obtained. The presented example illustrates the proposed approach.