矩阵的最大公因子的结构

Structure of Greatest Common Divisor of Matrix

提出任意两个方阵 A,B的行 (列 )最简形右 (左 )最大公因子的概念 .证明任意两个 n阶方阵A,B的行 (列 )最简形右 (左 )最大公因子的存在唯一性 ,利用行 (列 )最简形右 (左 )最大公因子给出了 A,B的所有右 (左 )最大公因子构成的集合的表示 ,给出求它们的简便方法 .最后将其推广至多个矩阵情形 .

The right (left) greatest common divisor in row (column) simplest form as a new concept is offered to arbitrary two square matrices A and B. The unique existence of right ( left) greatest common divisor in row (column) simplest form for arbitrary two square matrices A and B of n order is proved. By applying right (left) greatest common divisor in row (column) simplest form, the representation of the set constructed by all right (left) greatest divisors of A and B can be given, and the simple method for solving them can also be given. The concept is extended to the circumstance of multiple matrices.