定义在三个拟互素因子链上的倒数幂矩阵的非奇异性

华东师范大学学报(自然科学版) ›› 2013, Vol. 2013 ›› Issue (3): 164-168，175.

定义在三个拟互素因子链上的倒数幂矩阵的非奇异性

罗淼，谭千蓉

攀枝花学院~数学与计算机学院, 四川攀枝花 617000

收稿日期:2012-06-01 修回日期:2012-09-01 出版日期:2013-05-25 发布日期:2013-07-10

Nonsingularity of the reciprocal power matrices on three quasi-coprime divisor chains

LUO Miao, TAN Qian-rong

School of Mathematics and Computer Science, Panzhihua University, Panzhihua Sichuan 617000, China

Received:2012-06-01 Revised:2012-09-01 Online:2013-05-25 Published:2013-07-10

摘要/Abstract

摘要： 首先给出定义在三个拟互素因子链上的倒数幂~GCD~矩阵和倒数幂~LCM
矩阵的行列式的计算公式, 由此证明定义在三个拟互素因子链~$S$~上且~$S$
的最大公因子属于~$S$~时的倒数幂~GCD~矩阵和倒数幂~LCM~矩阵是非奇异的.
但当构成~$S$~的三个因子链不素时, 如此的结果不成立.

关键词: 三个拟互素因子链, 最大型因子, 倒数幂~GCD~矩阵, 倒数幂~LCM~矩阵

Abstract: The authors first obtained formulae for the determinants of
reciprocal power GCD matrix and reciprocal power LCM matrix defined
on a set $S$ consisting of three quasi-coprime divisor chains with
$\gcd (S)\in S$. Consequently, it was showed that the reciprocal
power GCD matrix and the reciprocal power LCM matrix defined on $S$
with $\gcd (S)\in S$ are nonsingular. But such result is not true
when $S$ consists of three divisor chains which are not
quasi-coprime.

Key words: three quasi-coprime divisor chains, greatest-type divisor, reciprocal power GCD matrix, reciprocal power LCM matrix

中图分类号:

O156.1

罗淼，谭千蓉. 定义在三个拟互素因子链上的倒数幂矩阵的非奇异性[J]. 华东师范大学学报(自然科学版), 2013, 2013(3): 164-168，175.

LUO Miao, TAN Qian-rong. Nonsingularity of the reciprocal power matrices on three quasi-coprime divisor chains[J]. Journal of East China Normal University(Natural Sc, 2013, 2013(3): 164-168，175.

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