| GCD闭集上的GCD幂矩阵和LCM幂矩阵 |
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| 引用本文： | 李竹宁 申泽淳. GCD闭集上的GCD幂矩阵和LCM幂矩阵[J]. 辽宁大学学报(自然科学版), 1998, 25(2): 101-105 |
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| 作者姓名： | 李竹宁 申泽淳 |
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| 作者单位： | 鞍钢职工工学院 |
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| 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。本文是交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ＬＣＭ幂矩阵和ＧＣＤ幂矩阵在ＧＣＤ闭集上的逆矩阵的漂亮结果。
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| 关 键 词： | GCD闭集 GCD幂矩阵 LCM幂矩阵 逆矩阵 |
GCD and LCM Power Matrices on GCD Closed Sets |
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| Li Zhuning Shen Zechun An Gang Engineering College,Anshan. GCD and LCM Power Matrices on GCD Closed Sets[J]. Journal of Liaoning University(Natural Sciences Edition), 1998, 25(2): 101-105 |
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| Authors: | Li Zhuning Shen Zechun An Gang Engineering College Anshan |
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| Affiliation: | Li Zhuning Shen Zechun An Gang Engineering College,Anshan 114002 |
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| Abstract: | 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. |
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| Keywords: | 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. |
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