Divisibility of LCM matrices by Totally nonnegative GCD matrices
Peeraphat Gatephan, Kijti Rodtes
TL;DR
This paper proves that totally nonnegative GCD matrices always divide their corresponding LCM matrices and introduces column monotone matrices to construct all such GCD matrices.
Contribution
It establishes a divisibility relation between GCD and LCM matrices for totally nonnegative cases and introduces column monotone matrices for their construction.
Findings
Totally nonnegative GCD matrices divide LCM matrices.
Introduction of column monotone matrices for constructing GCD matrices.
All totally nonnegative GCD matrices can be generated using these matrices.
Abstract
In this paper, we show that all totally nonnegative GCD matrices are always divisors of the corresponding LCM matrices in the ring . We also introduce \lq\lq column monotone matrices" used to construct all totally nonegative GCD matrices.
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