Smith meets Smith: Smith normal form of Smith matrix

DOI10.1080/03081081003709819zbMath1225.15014OpenAlexW2061228408MaRDI QIDQ3006568

Pauliina Ilmonen, Pentti Haukkanen

Publication date: 20 June 2011

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

Full work available at URL: https://doi.org/10.1080/03081081003709819

zbMATH Keywords

Smith determinantSmith normal formGCD matrixgreatest common divisor matrices

Mathematics Subject Classification ID

Determinants, permanents, traces, other special matrix functions (15A15) Arithmetic functions; related numbers; inversion formulas (11A25) Matrices of integers (15B36) Canonical forms, reductions, classification (15A21) Semilattices (06A12) Multiplicative structure; Euclidean algorithm; greatest common divisors (11A05) Matrices, determinants in number theory (11C20)

Related Items (1)

A topological approach to divisibility of arithmetical functions and GCD matrices

Cites Work

• The Smith normal form
• On eigenvalues of meet and join matrices associated with incidence functions
• On the divisibility of meet and join matrices
• Greatest common divisor matrices
• On greatest common divisor matrices and their applications
• On Smith's determinant
• On meet and join matrices associated with incidence functions.
• Eigenvalues and the Smith normal form
• Some characterizations of totients
• Reduction of Smith normal form transformation matrices
• On meet matrices on posets
• On Computing the Smith Normal Form of an Integer Matrix
• An analysis of GCD and LCM matrices via the LDL^T-factorization
• On Systems of Linear Diophantine Equations
• GCD matrices, posets, and nonintersecting paths
• Divisibility properties of Smith matrices

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