Divisibility among power GCD matrices and among power LCM matrices on finitely many coprime divisor chains

DOI10.1016/j.laa.2012.08.036zbMath1339.11041OpenAlexW2059312992WikidataQ112882204 ScholiaQ112882204MaRDI QIDQ1931754

Mao Li, Qianrong Tan

Publication date: 16 January 2013

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

Full work available at URL: https://doi.org/10.1016/j.laa.2012.08.036

zbMATH Keywords

matrix factorizationpower GCD matrixpower LCM matrixgreatest-type divisorcoprime divisor chainsmatrix divisibility

Mathematics Subject Classification ID

Matrices of integers (15B36) Matrices, determinants in number theory (11C20)

Related Items (11)

Divisibility among determinants of power matrices associated with integer-valued arithmetic functions ⋮ Determinants of matrices associated with arithmetic functions on finitely many quasi-coprime divisor chains ⋮ 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 ⋮ Further results on generalized LCM matrices ⋮ Non-divisibility of LCM matrices by GCD matrices on \(\gcd\)-closed sets ⋮ Divisibility of power LCM matrices by power GCD matrices on gcd-closed sets ⋮ ON THE DIVISIBILITY AMONG POWER LCM MATRICES ON GCD-CLOSED SETS

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• 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
• 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
• Notes on Hong's conjectures of real number power LCM matrices
• Divisibility properties of power GCD matrices and power LCM matrices
• 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
• Determinants of Smith matrices on three coprime divisor chains and divisibility
• Divisibility among power GCD matrices and among power LCM matrices on three coprime divisor chains
• Divisibility among power GCD matrices and among power LCM matrices on two coprime divisor chains II
• ASYMPTOTIC BEHAVIOR OF THE SMALLEST EIGENVALUE OF MATRICES ASSOCIATED WITH COMPLETELY EVEN FUNCTIONS (mod r)
• Determinants of multiplicative Toeplitz matrices
• Divisibility among power GCD matrices and among power LCM matrices on two coprime divisor chains
• On Hong’s conjecture for power LCM matrices
• A Generalization of Smith's Determinant
• Another generalisation of smith's determinant
• Note on some greatest common divisor matrices
• ASYMPTOTIC BEHAVIOR OF EIGENVALUES OF GREATEST COMMON DIVISOR 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 finitely many coprime divisor chains