摘要
１９８９年以来，多位国内外学者讨论过定义在集上的ＧＣＤ矩阵和ＬＣＭ矩阵，获得了一批成果．本文是将他们的研究推广到所谓ＧＣＤ幂矩阵和ＬＣＭ幂矩阵上，得到了这两类矩阵在ＧＣＤ闭集上的结构定理、行列式的计算公式，特别是得出了ＬＣＭ幂矩阵和ＧＣＤ幂矩阵在ＧＣＤ闭集上的逆矩阵的漂亮结果．
Since 1989, GCD and LCM matrices defined on sets have been studied by several scholars, a lot of results being obtained. In this paper we extended their studies to so called GCD and LCM power matrices. We presented the structure theorem and the formulas of computing the determinants of these matrices. Especially, we obtained the excellent results on the inversion of GCD and LCM power matrices on GCD closed sets. Many former conclusions are simply corollaries of this paper.
出处
《辽宁大学学报（自然科学版）》
CAS
1998年第2期101-105,共5页
Journal of Liaoning University：Natural Sciences Edition
关键词
GCD闭集
GCD幂矩阵
LCM幂矩阵
逆矩阵
GCD-closed set, Mobius inverse formula, GCD power matrices, LCM power matrices, The inverses of GCD and LCM matrices, Jordan's totient, The inverses of corelated matrices.
