An analysis of GCD and LCM matrices via the LDL^T-factorization

DOI10.13001/1081-3810.1121zbMath1042.15009OpenAlexW794566631MaRDI QIDQ4450711

Jeffrey S. Ovall

Publication date: 15 February 2004

Published in: The Electronic Journal of Linear Algebra (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/123680

zbMATH Keywords

algorithmdeterminantssingularityinertiapartially ordered sets\(\text{LDL}^T\)-factorizationGCD and LCM matricesreciprocal GCD and LCM matrices

Mathematics Subject Classification ID

Factorization of matrices (15A23) Determinants, permanents, traces, other special matrix functions (15A15) Combinatorics of partially ordered sets (06A07) Eigenvalues, singular values, and eigenvectors (15A18) Matrices of integers (15B36) Semilattices (06A12) Multiplicative structure; Euclidean algorithm; greatest common divisors (11A05)

Related Items (10)

Generalized eigenvalue problems for meet and join matrices on semilattices ⋮ Determinant and inverse of join matrices on two sets ⋮ On the positive definiteness and eigenvalues of meet and join matrices ⋮ On eigenvalues of meet and join matrices associated with incidence functions ⋮ Smith meets Smith: Smith normal form of Smith matrix ⋮ On unitary analogs of GCD reciprocal LCM matrices ⋮ Inertia, positive definiteness and \(\ell_p\) norm of GCD and LCM matrices and their unitary analogs ⋮ On meet hypermatrices and their eigenvalues ⋮ Studying the inertias of LCM matrices and revisiting the Bourque-Ligh conjecture ⋮ A lattice-theoretic approach to the Bourque–Ligh conjecture

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