On the factorization of LCM matrices on gcd-closed sets

DOI10.1016/S0024-3795(01)00499-2zbMath0995.15006WikidataQ127395936 ScholiaQ127395936MaRDI QIDQ1347956

Shao-Fang Hong

Publication date: 15 May 2002

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

Full work available at URL: http://www.mathematicsweb.org/pub/8/4/48/175/27/37/abstract.html

zbMATH Keywords

factorizationgcd-closed setgreatest common divisor matrixleast common multiple matrix

Mathematics Subject Classification ID

Factorization of matrices (15A23) Matrices of integers (15B36) Multiplicative structure; Euclidean algorithm; greatest common divisors (11A05) Matrices, determinants in number theory (11C20)

Related Items (28)

Divisibility among determinants of power matrices associated with integer-valued arithmetic functions ⋮ Determinants of Smith matrices on three coprime divisor chains and divisibility ⋮ 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 ⋮ LU-FACTORIZATIONS OF SYMMETRIC MATRICES WITH APPLICATIONS ⋮ On the divisibility among power GCD and power LCM matrices on gcd-closed sets ⋮ 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 ⋮ On the divisibility of meet and join matrices ⋮ Divisibility properties of power GCD matrices and power LCM matrices ⋮ 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 ⋮ Divisibility of LCM matrices by totally nonnegative GCD matrices ⋮ ASYMPTOTIC BEHAVIOR OF EIGENVALUES OF RECIPROCAL POWER LCM MATRICES ⋮ Non-divisibility of LCM matrices by GCD matrices on \(\gcd\)-closed sets ⋮ Determinants of Matrices Associated with Incidence Functions on Posets ⋮ On the divisibility of power LCM matrices by power GCD matrices ⋮ On Hong’s conjecture for power LCM matrices ⋮ 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 Nonsingular Power LCM Matrices ⋮ A topological approach to divisibility of arithmetical functions and GCD matrices ⋮ ON THE DIVISIBILITY AMONG POWER LCM MATRICES ON GCD-CLOSED SETS

Cites Work

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• The determinants of GCD matrices
• Greatest common divisor matrices
• Higher-dimensional gcd matrices
• On GCD and LCM matrices
• On LCM matrices on GCD-closed sets
• On the Bourque-Ligh conjecture of least common multiple matrices
• Matrices associated with classes of arithmetical functions
• Another generalisation of smith's determinant

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