Bézoutians of rational matrix functions, matrix equations and factorizations

DOI10.1016/S0024-3795(99)00068-3zbMath0958.15007WikidataQ114122536 ScholiaQ114122536MaRDI QIDQ1970435

Leonid Lerer, Leiba Rodman

Publication date: 19 March 2002

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

zbMATH Keywords

invariant subspacesmatrix equationsfactorizationsoperator methodsrealizationSylvester equationsBézoutiansrational matrix functionsdoubly coprime minimal factorizations

Mathematics Subject Classification ID

Factorization of matrices (15A23) Matrix equations and identities (15A24) Operator-theoretic methods (93B28) Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones) (47A56) Matrices over function rings in one or more variables (15A54)

Related Items

On a class of entire matrix function equations, Existence of minimal nonsquare \(J\)-symmetric factorizations for self-adjoint rational matrix functions., Bézout and Hankel matrices associated with row reduced matrix polynomials, Barnett type formulas

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Common minimal multiples and divisors for rational matrix functions
• Algebraic methods for Toeplitz-like matrices and operators
• Factored forms for solutions of \(AX-XB=C\) and \(X-AXB=C\) in companion matrices
• On the history of the Bézoutian and the resultant matrix
• Bezoutian and Schur-Cohn problem for operator polynomials
• Generalized Bézoutian and matrix equations
• Minimal factorization of matrix and operator functions
• Factorization of matrix functions and singular integral operators
• Interpolation of rational matrix functions
• Spectrum separation and inertia for operator polynomials
• Nonsingular solutions of TA-BT=C
• On the Routh-Hurwitz-Fujiwara and the Schur-Cohn-Fujiwara theorems for the root-separation problem
• On the effective computation of the inertia of a non-hermitian matrix
• \(J\)-pseudo-spectral and \(J\)-inner-pseudo-outer factorizations for matrix polynomials
• Bézoutians of rational matrix functions
• Bézoutians
• The Bezoutian and the eigenvalue-separation problem for matrix polynomials
• Rational matrix and operator functions with prescribed singularities
• Bezout operators for analytic operator functions. I: A general concept of Bezout operator
• Matrix representations of Bezoutians
• Inertia of operator polynomials and stability of differential equations
• Partially specified matrices and operators: classification, completion, applications
• Common zero structure of rational matrix functions
• Sylvester and Lyapunov equations and some interpolation problems for rational matrix functions
• Symmetric factorizations and localization of zeroes of rational matrix functions
• The Bezoutian and the algebraic Riccati equation
• The kernel of the bezoutian for operator Polynomials^∗
• The method of symmetric and Hermitian forms in the theory of the separation of the roots of algebraic equations
• Optimal Hankel Norm Model Reductions and Wiener–Hopf Factorization I: The Canonical Case
• Factorizations of Transfer Functions
• Inertia theorems for matrix polynomials
• Generalized Bezoutian and Sylvester matrices in multivariable linear control
• Greatest common divisor via generalized Sylvester and Bezout matrices
• On the Hermite-Fujiwara theorem in stability theory
• Invertible Solutions to the Operator Equation TA - BT = C
• AN OPERATOR GENERALIZATION OF THE LOGARITHMIC RESIDUE THEOREM AND THE THEOREM OF ROUCHÉ