Divisibility among power GCD matrices and among power LCM matrices on two coprime divisor chains
From MaRDI portal
Publication:3589202
DOI10.1080/03081080903008579zbMath1245.11037OpenAlexW4231203226MaRDI QIDQ3589202
Publication date: 20 September 2010
Published in: Linear and Multilinear Algebra (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1080/03081080903008579
Matrices of integers (15B36) Multiplicative structure; Euclidean algorithm; greatest common divisors (11A05) Matrices, determinants in number theory (11C20)
Related Items (14)
Divisibility among determinants of power matrices associated with integer-valued arithmetic functions ⋮ Determinants of Smith matrices on three coprime divisor chains and divisibility ⋮ 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 arithmetic functions on finitely many quasi-coprime divisor chains ⋮ Multiple divisor chains and determinants of matrices associated with completely even functions (modr) ⋮ 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 ⋮ Divisibility of matrices associated with multiplicative functions ⋮ Determinants and divisibility of power GCD and power LCM matrices on finitely many coprime divisor chains ⋮ Non-divisibility of LCM matrices by GCD matrices on \(\gcd\)-closed sets ⋮ Divisibility among power GCD matrices and among power LCM matrices on three coprime divisor chains ⋮ Divisibility 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
- Nonsingularity of matrices associated with classes of arithmetical functions
- Divisibility properties of power LCM matrices by power GCD matrices on gcd-closed sets
- 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
- Bounds for determinants of matrices associated with classes of arithmetical functions
- Notes on Hong's conjectures of real number power LCM matrices
- Divisibility properties of power GCD matrices and power LCM matrices
- Nonsingularity of matrices associated with classes of arithmetical functions on lcm-closed sets
- Nonsingularity of least common multiple matrices on gcd-closed sets
- Gcd-closed sets and determinants of matrices associated with arithmetical functions
- Determinants of Matrices Associated with Incidence Functions on Posets
- Determinants of multiplicative Toeplitz matrices
- On Nonsingular Power LCM Matrices
- 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 plqr
- Infinite divisibility of Smith matrices
- On the divisibility of power LCM matrices by power GCD matrices
- On Hong’s conjecture for power LCM matrices
- A Generalization of Smith's Determinant
- Another generalisation of smith's determinant
- 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
- ASYMPTOTIC BEHAVIOR OF EIGENVALUES OF RECIPROCAL POWER LCM MATRICES
- Divisibility properties of Smith matrices
- Diophantine Approximations and Hilbert's Space
This page was built for publication: Divisibility among power GCD matrices and among power LCM matrices on two coprime divisor chains
