Extended integer rank reduction formulas and Smith normal form

DOI10.1080/03081087.2012.743540zbMath1285.15007OpenAlexW2025136527MaRDI QIDQ2872529

Effat Golpar-Raboky, Nezam Mahdavi-Amiri

Publication date: 15 January 2014

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

Full work available at URL: https://doi.org/10.1080/03081087.2012.743540

zbMATH Keywords

factorizationinteger matrixSmith normal formmatrix decompositionscaled extended integer ABS algorithmsextended integer rank reduction formulageneral extended integer rank reducing processinteger biconjugation processinteger Wedderburn rank reduction formulascaled extended integer Abaffy-Broyden-Spedicato (ABS) class

Mathematics Subject Classification ID

Factorization of matrices (15A23) Quadratic and bilinear Diophantine equations (11D09) Algebraic number theory computations (11Y40) Linear Diophantine equations (11D04) Matrices of integers (15B36) Vector spaces, linear dependence, rank, lineability (15A03) Canonical forms, reductions, classification (15A21)

Related Items (3)

Real and integer Wedderburn rank reduction formulas for matrix decompositions ⋮ Real and Integer Extended Rank Reduction Formulas and Matrix Decompositions: A Review ⋮ Rank reduction processes for solving linear Diophantine systems and integer factorizations: a review

Cites Work

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• Extended rank reduction formulas containing Wedderburn and Abaffy-Broyden-Spedicato rank reducing processes
• Rank reduction, factorization and conjugation
• A comparative study of algorithms for computing the Smith normal form of an integer matrix†
• A Rank–One Reduction Formula and Its Applications to Matrix Factorizations
• A class of ABS algorithms for Diophantine linear systems

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