整数矩阵可嵌入整数环上的可逆矩阵的充要条件

Necessary and sufficient condition for an integral matrix to be embeddable in a reversible matrix on the integral ring

整数环上的可逆矩阵的任意具有相同行(或列)的同阶子式互素,整数矩阵A可嵌入整数环上的可逆 矩阵的充要条件为A存在两个代数余子式互素.给出了2阶、3阶整数环上的可逆矩阵的构造的简便方法.

If A is a reversible matrix on the integral ring, its minors on the same rows or columns are relative prime. The necessary and sufficient condition for an integral matrix A to be embeddable in a reversible matrix on the integral ring is two algebraic cofactors of A relatively priming. A handy way of the formation of a 2 or 3 step reversible matrix on the integral ring is given.