On Nonsingular Power LCM Matrices

DOI10.1142/S1005386706000642zbMath1140.11319MaRDI QIDQ3421815

Qi Sun, Kar Ping Shum, Shao-Fang Hong

Publication date: 8 February 2007

Published in: Algebra Colloquium (Search for Journal in Brave)

zbMATH Keywords

nonsingularitypower LCM matrixgreatest-type divisorGCD-closed setLCM-closed set

Mathematics Subject Classification ID

Arithmetic functions; related numbers; inversion formulas (11A25) Matrices, determinants in number theory (11C20)

Related Items (15)

ASYMPTOTIC BEHAVIOR OF THE SMALLEST EIGENVALUE OF MATRICES ASSOCIATED WITH COMPLETELY EVEN FUNCTIONS (mod r) ⋮ LU-FACTORIZATIONS OF SYMMETRIC MATRICES WITH APPLICATIONS ⋮ Divisibility of determinants of power GCD matrices and power LCM matrices on finitely many quasi-coprime divisor chains ⋮ ASYMPTOTIC BEHAVIOR OF LARGEST EIGENVALUE OF MATRICES ASSOCIATED WITH COMPLETELY EVEN FUNCTIONS (MOD r) ⋮ THERE DOES NOT EXIST AN ODD SINGULAR NUMBER OF THE FORM p^lqr ⋮ Determinants and divisibility of power GCD and power LCM matrices on finitely many coprime divisor chains ⋮ Notes on Hong's conjectures of real number power LCM matrices ⋮ Divisibility among power GCD matrices and among power LCM matrices on two coprime divisor chains ⋮ Nonsingularity of matrices associated with classes of arithmetical functions on lcm-closed sets ⋮ ASYMPTOTIC BEHAVIOR OF EIGENVALUES OF RECIPROCAL POWER LCM MATRICES ⋮ Power GCD Matrices for a UFD ⋮ Divisibility among power GCD matrices and among power LCM matrices on three coprime divisor chains ⋮ GCD-closed sets and divisibility of Smith matrices ⋮ Divisibility properties of power LCM matrices by power GCD matrices on gcd-closed sets ⋮ A topological approach to divisibility of arithmetical functions and GCD matrices

Cites Work

• 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 GCD and LCM 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
• Matrices associated with multiplicative functions
• Arithmetical properties of generalized Ramanujan sums
• Nonsingularity of least common multiple matrices on gcd-closed sets
• Gcd-closed sets and determinants of matrices associated with arithmetical functions
• A Generalization of Smith's Determinant
• Lower bounds for determinants of matrices associated with classes of arithmetical Functions
• Matrices associated with arithmetical functions
• ASYMPTOTIC BEHAVIOR OF EIGENVALUES OF GREATEST COMMON DIVISOR MATRICES
• Notes on power LCM matrices
• Factorization of matrices associated with classes of arithmetical functions
• Diophantine Approximations and Hilbert's Space

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