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Divisibility of LCM matrices by totally nonnegative GCD matrices. (English) Zbl 1464.15021

Summary: 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 “column monotone matrices” used to construct all totally nonnegative GCD matrices.

MSC:

15A23 Factorization of matrices
15B48 Positive matrices and their generalizations; cones of matrices
15A15 Determinants, permanents, traces, other special matrix functions
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