On the eigenvalues of certain number-theoretic matrices

zbMath1275.15012arXiv1309.0320MaRDI QIDQ4914877

Pentti Haukkanen, Mika Mattila

Publication date: 15 April 2013

Full work available at URL: https://arxiv.org/abs/1309.0320

zbMATH Keywords

eigenvaluegreatest common divisorleast common multipleSmith's determinantmatrix normGCD matrixLCM matrix

Mathematics Subject Classification ID

Factorization of matrices (15A23) Inequalities involving eigenvalues and eigenvectors (15A42) Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Arithmetic functions; related numbers; inversion formulas (11A25) Multiplicative structure; Euclidean algorithm; greatest common divisors (11A05) Matrices, determinants in number theory (11C20)

Related Items (6)

Matrices with multiplicative entries are tensor products ⋮ Spectral asymptotics for a family of LCM matrices ⋮ On a conjecture of Ilmonen, Haukkanen and Merikoski concerning the smallest eigenvalues of certain GCD related matrices ⋮ Bounds on the spectrum of nonsingular triangular \((0,1)\)-matrices ⋮ On the eigenvalues of combined meet and join matrices ⋮ A proof of a conjecture on monotonic behavior of the smallest and the largest eigenvalues of a number theoretic matrix

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