MOBIUS变换与GCD函数矩阵（Ⅱ）

Mobius Transforms and GCD Function Matrices (Ⅱ)

本文作为ＭＢＩＵＳ变换与ＧＣＤ函数矩阵（Ⅰ）的续篇，继续讨论在ＧＣＤ闭集上的函数矩阵（ｆ（Ｓ））及其行列式的计算方法．特别是我们用组合学的方法，求得了定义在集Ｓ上的Ｍｂｉｕｓ矩阵，它推广了数论中的Ｍｂｉｕｓ函数μ．从而求得了（ｆ（Ｓ））的逆矩阵．

As the continuation of Part (Ⅰ), we discussed the function matrix (f(S) ) defined on S and the computing method of its determinant in this paper. Making use of a method of combinatorics, we obtained the Mobius matrix on S, which is a generalization of M obius function in the theory of numbers. Thus the inverse matrix of (f(S)) is found.