On inverses of GCD matrices associated with multiplicative functions and a proof of the Hong-Loewy conjecture

DOI10.1016/j.laa.2008.10.025zbMath1216.11032OpenAlexW1984465114WikidataQ122975070 ScholiaQ122975070MaRDI QIDQ999809

Ercan Altinisik

Publication date: 10 February 2009

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2008.10.025

zbMATH Keywords

Riemann zeta functioneigenvaluesEuler productsmultiplicative functionsmatrix normsGCD matrices

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Eigenvalues, singular values, and eigenvectors (15A18) Matrices of integers (15B36) Matrices, determinants in number theory (11C20)

Related Items (7)

Divisibility among power matrices associated with classes of arithmetic functions ⋮ Divisibility among power matrices associated with arithmetic functions on finitely many quasi-coprime divisor chains ⋮ Determinant and inverse of join matrices on two sets ⋮ On a conjecture of Ilmonen, Haukkanen and Merikoski concerning the smallest eigenvalues of certain GCD related matrices ⋮ On the positive definiteness and eigenvalues of meet and join matrices ⋮ A proof of a conjecture on monotonic behavior of the smallest and the largest eigenvalues of a number theoretic matrix ⋮ GCD-closed sets and divisibility of Smith matrices

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