Bounds for determinants of matrices associated with classes of arithmetical functions

DOI10.1016/S0024-3795(98)10052-6zbMath0937.15004MaRDI QIDQ1808961

Shao-Fang Hong

Publication date: 28 May 2000

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

zbMATH Keywords

greatest common divisorleast common multiplearithmetical functionbounds for determinants

Mathematics Subject Classification ID

Determinants, permanents, traces, other special matrix functions (15A15) Miscellaneous inequalities involving matrices (15A45) Arithmetic functions; related numbers; inversion formulas (11A25)

Related Items (13)

Injectivity and surjectivity of Collatz functions ⋮ Lower bounds for determinants of matrices associated with classes of arithmetical Functions ⋮ ASYMPTOTIC BEHAVIOR OF THE SMALLEST EIGENVALUE OF MATRICES ASSOCIATED WITH COMPLETELY EVEN FUNCTIONS (mod r) ⋮ LU-FACTORIZATIONS OF SYMMETRIC MATRICES WITH APPLICATIONS ⋮ On meet and join matrices associated with incidence functions. ⋮ ASYMPTOTIC BEHAVIOR OF LARGEST EIGENVALUE OF MATRICES ASSOCIATED WITH COMPLETELY EVEN FUNCTIONS (MOD r) ⋮ On the positive definiteness and eigenvalues of meet and join matrices ⋮ Bounds for determinants of meet matrices associated with incidence functions ⋮ Nonsingularity of matrices associated with classes of arithmetical functions ⋮ Divisibility among power GCD matrices and among power LCM matrices on two coprime divisor chains ⋮ ASYMPTOTIC BEHAVIOR OF EIGENVALUES OF RECIPROCAL POWER LCM MATRICES ⋮ Divisibility among power GCD matrices and among power LCM matrices on three coprime divisor chains ⋮ Reciprocal power GCDQ matrices and power LCMQ matrices defined on factor closed sets over Euclidean domains

Cites Work

• The determinants of GCD matrices
• Inertia characteristics of self-adjoint matrix polynomials
• Greatest common divisor matrices
• On greatest common divisor matrices and their applications
• On GCD and LCM matrices
• Matrices associated with classes of arithmetical functions
• Matrices associated with multiplicative functions
• Semi-multiplicative functions
• Matrix Analysis
• Another generalisation of smith's determinant
• Matrices associated with arithmetical functions
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