On a conjecture of Ilmonen, Haukkanen and Merikoski concerning the smallest eigenvalues of certain GCD related matrices

DOI10.1016/j.laa.2015.11.023zbMath1334.15079OpenAlexW2231083823WikidataQ123019460 ScholiaQ123019460MaRDI QIDQ905699

N. E. Zubov

Publication date: 28 January 2016

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

Full work available at URL: https://doi.org/10.1016/j.laa.2015.11.023

zbMATH Keywords

eigenvaluespectral radius\((0,1)\)-matrixpositive matrixFibonacci numberGCD matrix

Mathematics Subject Classification ID

Factorization of matrices (15A23) Eigenvalues, singular values, and eigenvectors (15A18) Positive matrices and their generalizations; cones of matrices (15B48) Matrices of integers (15B36) Fibonacci and Lucas numbers and polynomials and generalizations (11B39) Matrices, determinants in number theory (11C20)

Related Items (5)

Generalized eigenvalue problems for meet and join matrices on semilattices ⋮ Bounds on the spectrum of nonsingular triangular \((0,1)\)-matrices ⋮ On the smallest singular value in the class of invertible lower triangular \((0,1)\) matrices ⋮ On the smallest singular value in the class of unit lower triangular matrices with entries in \([-a, a\)] ⋮ Lower bounds for the largest eigenvalue of the gcd matrix on {1, 2,..., n}

Uses Software

• OEIS

Cites Work

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• Diophantine Approximations and Hilbert's Space

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