GCD矩阵和LCM矩阵的性质

ON THE PROPERTIES OF GCD AND LCM MATRICES

设S＝｛x1，x2，…，xn｝是含n个不同正整数的集合，（S）、［S］分别是定义在S上的GCD矩阵和LCM矩阵．给出了对偶因数封闭集的定义，讨论了对偶因数封闭集和最小公倍数封闭集上的矩阵（S）和［S］的性质．

Let S={x1, x2, …, xn} be a set of distinct positive integers, (S) and [S] are GCD and LCM matrices defined on S. Dual factor closed set is defined and the properties of GCD and LCM matrices defined on dual factor closed set and least common multiple cioed set are discussed.