Matrices associated with arithmetical functions

DOI10.1080/03081089308818225zbMath0815.15022OpenAlexW2022131401MaRDI QIDQ4322540

Keith Bourque, Steve Ligh

Publication date: 9 July 1995

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

Full work available at URL: https://doi.org/10.1080/03081089308818225

zbMATH Keywords

greatest common divisordeterminantinversearithmetical functionpositive definiteGCD matrix

Mathematics Subject Classification ID

Determinants, permanents, traces, other special matrix functions (15A15) Arithmetic functions; related numbers; inversion formulas (11A25) Matrices of integers (15B36) Matrices, determinants in number theory (11C20)

Related Items (50)

Divisibility among determinants of power matrices associated with integer-valued arithmetic functions ⋮ Determinants of Smith matrices on three coprime divisor chains and divisibility ⋮ Lower bounds for determinants of matrices associated with classes of arithmetical Functions ⋮ Determinants of matrices associated with arithmetic functions on finitely many quasi-coprime divisor chains ⋮ ASYMPTOTIC BEHAVIOR OF THE SMALLEST EIGENVALUE OF MATRICES ASSOCIATED WITH COMPLETELY EVEN FUNCTIONS (mod r) ⋮ Divisibility among power matrices associated with classes of arithmetic functions ⋮ Multiple gcd-closed sets and determinants of matrices associated with arithmetic functions ⋮ LU-FACTORIZATIONS OF SYMMETRIC MATRICES WITH APPLICATIONS ⋮ On Smith's determinant ⋮ 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 ⋮ Generalized eigenvalue problems for meet and join matrices on semilattices ⋮ 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 ⋮ Three families of matrices ⋮ On meet and join matrices associated with incidence functions. ⋮ ASYMPTOTIC BEHAVIOR OF LARGEST EIGENVALUE OF MATRICES ASSOCIATED WITH COMPLETELY EVEN FUNCTIONS (MOD r) ⋮ Divisibility of matrices associated with multiplicative functions ⋮ Further results on generalized LCM matrices ⋮ Determinant and inverse of meet and join matrices ⋮ On the positive definiteness and eigenvalues of meet and join matrices ⋮ Bounds on the spectrum of nonsingular triangular \((0,1)\)-matrices ⋮ On a general form of meet matrices associated with incidence functions ⋮ Determinants and divisibility of power GCD and power LCM matrices on finitely many coprime divisor chains ⋮ On eigenvalues of meet and join matrices associated with incidence functions ⋮ Notes on Hong's conjectures of real number power LCM matrices ⋮ Divisibility properties of power GCD matrices and power LCM matrices ⋮ Explicit expressions of Smith's determinant on a poset ⋮ Nonsingularity of matrices associated with classes of arithmetical functions ⋮ 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 ⋮ Inertia, positive definiteness and \(\ell_p\) norm of GCD and LCM matrices and their unitary analogs ⋮ Non-divisibility of LCM matrices by GCD matrices on \(\gcd\)-closed sets ⋮ On inverses of GCD matrices associated with multiplicative functions and a proof of the Hong-Loewy conjecture ⋮ Determinants of Matrices Associated with Incidence Functions on Posets ⋮ Meet and join matrices in the poset of exponential divisors ⋮ On the divisibility of power LCM matrices by power GCD matrices ⋮ On meet hypermatrices and their eigenvalues ⋮ Matrices associated with multiplicative functions ⋮ Bounds for determinants of matrices associated with classes of arithmetical functions ⋮ 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 ⋮ On meet matrices on posets ⋮ On Nonsingular Power LCM Matrices ⋮ Some analogues of smith's determinant ⋮ ON THE DIVISIBILITY AMONG POWER LCM MATRICES ON GCD-CLOSED SETS

Cites Work

• The determinants of GCD matrices
• Greatest common divisor matrices
• Higher-dimensional gcd matrices
• On GCD and LCM matrices
• A Generalization of Smith's Determinant
• Another generalisation of smith's determinant
• Unnamed Item

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