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

LUO Miao; TAN Qian-rong

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Jul. 2013

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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 Sciences), 2013, (3): 164-168，175.

Citation:

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 Sciences), 2013, (3): 164-168，175.

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

1.
School of Mathematics and Computer Science, Panzhihua University, Panzhihua Sichuan 617000, China

Received Date: 2012-06-01
Rev Recd Date: 2012-09-01
Publish Date: 2013-05-25

Abstract

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.
- three quasi-coprime divisor chains,
- greatest-type divisor,
- reciprocal power GCD matrix,
- reciprocal power LCM matrix

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References(1)

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