A note on the local-global principle for similarity of matrices

DOI10.1016/0024-3795(80)90197-4zbMath0442.15009OpenAlexW1989345116MaRDI QIDQ1143464

Robert M. Guralnick

Publication date: 1980

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

Full work available at URL: https://doi.org/10.1016/0024-3795(80)90197-4

zbMATH Keywords

similarity of matricesmatrices over an integral domain

Mathematics Subject Classification ID

Matrices over special rings (quaternions, finite fields, etc.) (15B33)

Related Items (12)

Computation of lattice isomorphisms and the integral matrix similarity problem ⋮ The critical groups of the Peisert graphs ⋮ Similarity of holomorphic matrices ⋮ On conjugacy of diagonalizable integral matrices ⋮ Similarity classes for nilpotent operators over Dedekind domains ⋮ Similarity of matrices over local rings ⋮ On similarities of class \(C^ p\) and applications to matrix differential equations ⋮ Local to global equivalence for homomorphisms ⋮ Globally analytic triangularization of a matrix function ⋮ Block conjugacy of irreducible toral automorphisms ⋮ Composition of binary integral quadratic forms via integral 2 × 2 matrices and composition of matrix classes ⋮ The pointwise-local-global principle for solutions of generic linear equations

Cites Work

• Equivalence of representations under extensions of local ground rings
• On holomorphically similar matrices
• On pointwise and analytic similarity of matrices
• A diophantine problem arising out of similarity classes of integral matrices
• Matrices similar on a Zariski-open set
• Algebraic integral representations by arbitrary forms
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