Simultaneous reduction to companion and triangular forms of sets of matrices

DOI10.1080/03081089008817981zbMath0716.15011OpenAlexW2022960192MaRDI QIDQ3203158

Harm Bart, G. Philip. A. Thijsse

Publication date: 1990

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

Full work available at URL: https://doi.org/10.1080/03081089008817981

zbMATH Keywords

complex matricescompanion formsrational matrix functionscomplementary triangular formscomplete factorizationsimultaneous reduction under similarityupper triangular forms

Mathematics Subject Classification ID

Canonical forms, reductions, classification (15A21)

Related Items

Pairs of companion matrices and their simultaneous reduction to complementary triangular forms, Simultaneous reduction to triangular and companion forms of pairs of matrices: The case \(rank(I-AZ)=1\), Spectral criteria for complementary triangular forms, Bilinear characterizations of companion matrices, Symmetry properties of and reduction principles for divisibility relations between the invariant factors of products of holomorphic matrix functions, Simultaneous reduction to triangular forms after extension with zeroes, Similarity invariants for pairs of upper triangular Toeplitz matrices, Companion based matrix functions: Description and minimal factorization, Factorization and job scheduling: A connection via companion based matrix functions, Quasicomplete factorization and the two machine flow shop problem

Cites Work

• Simultaneous equations models in applied search theory
• Simultaneous reduction of sets of matrices under similarity
• Transfer functions and operator theory
• Complementary triangular forms of pairs of matrices, realizations with prescribed main matrices, and complete factorization of rational matrix functions
• Upper triangularization of matrices by lower triangular similarities
• Operator polynomials as inverses of characteristic functions
• Factorizations of Transfer Functions
• Simultaneous triangularization of matrices—low rank cases and the nonderogatory case
• The Simultaneous Reduction of Two Matrices to Triangle Form
• On the characteristic roots of matric polynomials