On eigenvalues of meet and join matrices associated with incidence functions

DOI10.1016/j.laa.2008.04.014zbMath1143.15016OpenAlexW1977184399MaRDI QIDQ932156

Pentti Haukkanen, Pauliina Ilmonen, Jorma Kaarlo Merikoski

Publication date: 10 July 2008

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

Full work available at URL: https://doi.org/10.1016/j.laa.2008.04.014

zbMATH Keywords

meet matrixSmith determinantGCD matrixjoin matrixLCM matrix

Mathematics Subject Classification ID

Inequalities involving eigenvalues and eigenvectors (15A42) Matrices of integers (15B36) Semilattices (06A12)

Related Items (13)

Generalized eigenvalue problems for meet and join matrices on semilattices ⋮ 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 ⋮ Bounds on the spectrum of nonsingular triangular \((0,1)\)-matrices ⋮ On the eigenvalues of combined meet and join 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 \([-a, a\)] ⋮ Smith meets Smith: Smith normal form of Smith matrix ⋮ A proof of a conjecture on monotonic behavior of the smallest and the largest eigenvalues of a number theoretic matrix ⋮ On unitary analogs of GCD reciprocal LCM matrices ⋮ On inverses of GCD matrices associated with multiplicative functions and a proof of the Hong-Loewy conjecture ⋮ On meet hypermatrices and their eigenvalues

Cites Work

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• ASYMPTOTIC BEHAVIOR OF EIGENVALUES OF GREATEST COMMON DIVISOR MATRICES
• Infinitely Divisible Matrices
• Diophantine Approximations and Hilbert's Space
• Bounds for determinants of meet matrices associated with incidence functions

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