Complementary triangular forms of pairs of matrices, realizations with prescribed main matrices, and complete factorization of rational matrix functions

DOI10.1016/0024-3795(88)90228-5zbMath0645.15012OpenAlexW2013102415MaRDI QIDQ1103024

B. George

Publication date: 1988

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

Full work available at URL: https://doi.org/10.1016/0024-3795(88)90228-5

zbMATH Keywords

transfer functionsimultaneous reductiontriangular matrixminimal factorizationcomplementary triangular formscomplete factorization

Mathematics Subject Classification ID

Factorization of matrices (15A23) Hermitian, skew-Hermitian, and related matrices (15B57)

Related Items (15)

Pairs of companion matrices and their simultaneous reduction to complementary triangular forms ⋮ Upper triangularization of matrices by lower triangular similarities ⋮ Upper triangular similarity of upper triangular matrices ⋮ Simultaneous reduction to triangular and companion forms of pairs of matrices: The case \(rank(I-AZ)=1\) ⋮ Upper triangularization of matrices by permutations and lower triangular similarity transformations ⋮ Simultaneous reduction to companion and triangular forms of sets of matrices ⋮ On the deformation of linear Hamiltonian systems ⋮ Spectral criteria for complementary triangular forms ⋮ Quasicomplete factorizations of rational matrix functions ⋮ Pairs of matrices which do not admit a complementary triangular form ⋮ 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

• Common eigenvectors of two matrices
• Inertia characteristics of self-adjoint matrix polynomials
• Simultaneous reduction of sets of matrices under similarity
• Transfer functions and operator theory
• Upper triangularization of matrices by lower triangular similarities
• Minimal factorization of matrix and operator functions
• Fast projection methods for minimal design problems in linear system theory
• Factorizations of Transfer Functions
• Simultaneous triangularization of matrices—low rank cases and the nonderogatory case
• Mathematical Description of Linear Dynamical Systems
• On the characteristic roots of matric polynomials
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