On similarity of matrices over commutative rings

DOI10.1016/j.laa.2004.11.015zbMath1073.15009OpenAlexW1964909950MaRDI QIDQ1772732

Volodymyr M. Prokip

Publication date: 21 April 2005

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

Full work available at URL: https://doi.org/10.1016/j.laa.2004.11.015

zbMATH Keywords

eigenvalueeigenvectorcompanion matrixfactorizationmatrix similaritydiagonal matrix

Mathematics Subject Classification ID

Factorization of matrices (15A23) Matrices over special rings (quaternions, finite fields, etc.) (15B33) Canonical forms, reductions, classification (15A21)

Related Items (7)

Diagonalization of matrices over the domain of principal ideals with minimal polynomial \(m(\lambda )=(\lambda -\alpha )(\lambda -\beta)\), \(\alpha\neq\beta\) ⋮ Diagonalizability of matrices over a principal ideal domain ⋮ Affine Mendelsohn triple systems and the Eisenstein integers ⋮ Diagonability of matrices over commutative semirings ⋮ Recursive MDS matrices over finite commutative rings ⋮ Structure of Rank-One Matrices Over the Domain of Principal Ideals Relative to Similarity Transformations ⋮ On the similarity of certain integer matrices with single eigenvalue over the ring of integers

Cites Work

• Simultaneous diagonalization of an algebraic family of matrices
• Diagonalization of matrices over regular rings
• Simultaneous reduction to triangular forms after extension with zeroes
• Diagonalization Over Commutative Rings
• Equivalence of partitioned matrices
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