ASYMPTOTIC BEHAVIOR OF EIGENVALUES OF RECIPROCAL POWER LCM MATRICES

DOI10.1017/S0017089507003953zbMath1186.11011OpenAlexW2115375406MaRDI QIDQ5444676

K. S. Enoch Lee, Shao-Fang Hong

Publication date: 25 February 2008

Published in: Glasgow Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0017089507003953

zbMATH Keywords

eigenvalueSmith determinantGCD matrixLCM matrix

Mathematics Subject Classification ID

Eigenvalues, singular values, and eigenvectors (15A18) Matrices of integers (15B36) Matrices, determinants in number theory (11C20)

Related Items (32)

Divisibility among determinants of power matrices associated with integer-valued arithmetic functions ⋮ Determinants of Smith matrices on three coprime divisor chains and divisibility ⋮ On a certain determinant for a U.F.D. ⋮ 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 ⋮ Multiple gcd-closed sets and determinants of matrices associated with arithmetic functions ⋮ Multiple divisor chains and determinants of matrices associated with completely even functions (modr) ⋮ On the divisibility among power GCD and power LCM matrices on gcd-closed sets ⋮ Determinant and inverse of join matrices on two sets ⋮ Divisibility among power GCD matrices and among power LCM matrices on finitely many coprime divisor chains ⋮ Divisibility of determinants of power GCD matrices and power LCM matrices on finitely many quasi-coprime divisor chains ⋮ Spectral asymptotics for a family of LCM matrices ⋮ Upper bounds for the condition numbers of the GCD and the reciprocal GCD matrices in spectral norm ⋮ Three families of matrices ⋮ On a conjecture of Ilmonen, Haukkanen and Merikoski concerning the smallest eigenvalues of certain GCD related matrices ⋮ On a certain arithmetical determinant ⋮ Divisibility of matrices associated with multiplicative functions ⋮ On the positive definiteness and eigenvalues of meet and join matrices ⋮ Bounds on the spectrum of nonsingular triangular \((0,1)\)-matrices ⋮ Determinants and divisibility of power GCD and power LCM matrices on finitely many coprime divisor chains ⋮ On the eigenvalues of combined meet and join matrices ⋮ Notes on Hong's conjectures of real number power LCM matrices ⋮ The least common multiple of consecutive arithmetic progression terms ⋮ Divisibility properties of power GCD matrices and power LCM matrices ⋮ A proof of a conjecture on monotonic behavior of the smallest and the largest eigenvalues of a number theoretic matrix ⋮ Divisibility among power GCD matrices and among power LCM matrices on two coprime divisor chains ⋮ Inertia, positive definiteness and \(\ell_p\) norm of GCD and LCM matrices and their unitary analogs ⋮ On inverses of GCD matrices associated with multiplicative functions and a proof of the Hong-Loewy conjecture ⋮ Divisibility among power GCD matrices and among power LCM matrices on three coprime divisor chains ⋮ GCD-closed sets and divisibility of Smith matrices ⋮ Divisibility of power LCM matrices by power GCD matrices on gcd-closed sets ⋮ Divisibility properties of power LCM matrices by power GCD matrices on gcd-closed sets

Cites Work

• Unnamed Item
• Unnamed Item
• A Hilbert space of Dirichlet series and systems of dilated functions in \(L^ 2(0,1)\)
• Nonsingularity of matrices associated with classes of arithmetical functions
• Greatest common divisor matrices
• On the Bourque-Ligh conjecture of least common multiple matrices
• Matrices associated with classes of arithmetical functions
• On the factorization of LCM matrices on gcd-closed sets
• On Smith's determinant
• On meet and join matrices associated with incidence functions.
• Matrices associated with multiplicative functions
• Bounds for determinants of matrices associated with classes of arithmetical functions
• Notes on Hong's conjectures of real number power LCM matrices
• Nonsingularity of matrices associated with classes of arithmetical functions on lcm-closed sets
• Arithmetical properties of generalized Ramanujan sums
• Nonsingularity of least common multiple matrices on gcd-closed sets
• Notes on the divisibility of GCD and LCM matrices
• On Nonsingular Power LCM Matrices
• On the divisibility of power LCM matrices by power GCD matrices
• On Hong’s conjecture for power LCM matrices
• Matrix Analysis
• A Generalization of Smith's Determinant
• Matrices associated with arithmetical functions
• ASYMPTOTIC BEHAVIOR OF EIGENVALUES OF GREATEST COMMON DIVISOR MATRICES
• GCD matrices, posets, and nonintersecting paths
• Diophantine Approximations and Hilbert's Space

This page was built for publication: ASYMPTOTIC BEHAVIOR OF EIGENVALUES OF RECIPROCAL POWER LCM MATRICES