Divisibility of LCM matrices by Totally nonnegative GCD matrices

Published 2 Nov 2020 in math.RA | (2011.00863v1)

Abstract: In this paper, we show that all totally nonnegative GCD matrices are always divisors of the corresponding LCM matrices in the ring $\mathbb{M}_{n}(\mathbb{Z})$. We also introduce \lq\lq column monotone matrices" used to construct all totally nonegative GCD matrices.

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