四川大学学报（自然科学版）2012，Vol.49Issue(5)：965-969,5.DOI:10.3969/j.issn.0490-6756.2012.05.005
两个拟互素因子链上倒数幂GCD与倒数幂LCM矩阵的非奇异性
Nonsingularity of the reciprocal power GCD matrices and the reciprocal power LCM matrices on two quasi-coprime divisor chains
摘要
Abstract
Let S={x1,x2,…,xn} be a set of n distinct positive integers and a≥0 be a real number. The matrix having theath power1/(xi,xj)a as its (xi,xj) -entry is called reciprocal power greatest common divisor (GCD) matrix defined on S, denoted by (1/Sa) where (xi,xj)a = (gcd(xi,xj))a. Similarly we can define reciprocal power LCM matrix [1/Sa] on S. In this paper, the authors first obtain formulaes for the determinants of reciprocal power GCD matrix and reciprocal power LCM matrix defined on S which consists of two quasi-coprime divisor chains and gcd(S) € S. Then they show that the reciprocal power GCD matrix and the reciprocal power LCM matrix defined on two quasi-coprime divisor chains S with gcd(S) € S are nonsingular.关键词
拟互素因子链/最大型因子/倒数幂GCD矩阵/倒数幂LCM矩阵Key words
quasi-coprime divisor chain/ greatest-type divisor/ reciprocal power GCD matrix/ reciprocal power LCM matrix (2000 MSC 11C20/ 11A05/ 15A36)分类
数理科学引用本文复制引用
林宗兵,谭千蓉..两个拟互素因子链上倒数幂GCD与倒数幂LCM矩阵的非奇异性[J].四川大学学报（自然科学版）,2012,49(5):965-969,5.基金项目
国家自然科学基金(10971145) （10971145）
攀枝花市应用技术研究与开发项目(2012CY-G-26) （2012CY-G-26）
