Journal of East China Normal University(Natural Sc ›› 2013, Vol. 2013 ›› Issue (3): 164-168,175.

• Article • Previous Articles     Next Articles

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

LUO Miao, TAN Qian-rong   

  1. 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

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

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

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