Existence of minimal nonsquare \(J\)-symmetric factorizations for self-adjoint rational matrix functions.

DOI10.1016/S0024-3795(03)00457-9zbMath1059.47012WikidataQ114122581 ScholiaQ114122581MaRDI QIDQ1426297

André C. M. Ran, Leonid Lerer, Mark Adam Petersen

Publication date: 14 March 2004

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

zbMATH Keywords

Riccati equationscommon zerossymmetric factorizationrational matrix functionsminimal factorizationsBezoutians

Mathematics Subject Classification ID

Matrix equations and identities (15A24) Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones) (47A56) Factorization theory (including Wiener-Hopf and spectral factorizations) of linear operators (47A68)

Related Items

Necessary and sufficient conditions for existence of \(J\)-spectral factorization for para-Hermitian rational matrix functions

Cites Work

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• An alternative proof for the minimal factorization theorem for rational matrices
• Minimal square spectral factors
• Parametrization of all minimal square spectral factors
• On minimial factorizations of rational matrix functions
• On symmetric rational transfer functions
• Stable invariant Lagrangian subspaces: Factorization of symmetric rational matrix functions and other applications
• Matrices and indefinite scalar products
• Constructive methods of Wiener-Hopf factorization
• Boundary value problems in abstract kinetic theory
• Spectral factorization via Hermitian pencils
• Minimal factorization of matrix and operator functions
• Factorization of matrix functions and singular integral operators
• Minimal factorization of selfadjoint rational matrix functions
• On self-adjoint matrix polynomials with constant signature
• Minimal nonsquare \(J\)-spectral factorization, generalized Bezoutians and common zeros for rational matrix functions
• Minimal nonsquare spectral factors
• Nonsquare spectral factors via factorizations of a unitary function
• Bézoutians of rational matrix functions
• Common zero structure of rational matrix functions
• Bézoutians of rational matrix functions, matrix equations and factorizations
• Rational spectral factorization using state-space methods
• Minimal Square Spectral Factors via Triples
• Symmetric factorizations and localization of zeroes of rational matrix functions
• Systems of integral equations on a half line with kernels depending on the difference of arguments
• AJ-Spectral Factorization Approach to $\mathcal{H}_\infty $
• On symmetric factorizations of rational matrix functions
• Forward and backward semimartingale models for gaussian processes with stationary increments
• Optimal Hankel Norm Model Reductions and Wiener–Hopf Factorization I: The Canonical Case
• On factorizations of rational matrices
• Factorizations of Transfer Functions
• Factorization of selfadjoint matrix polynomials with constant signature
• A characterization of minimal square spectral factors
• On the Lyapunov equation, coinvariant subspaces and some problems related to spectral factorizations
• Zeros of Spectral Factors, the Geometry of Splitting Subspaces, and the Algebraic Riccati Inequality
• A State-Space Approach to Indefinite Spectral Factorization
• On a Hardy space approach to the analysis of spectral factors
• The Stabilizing Solution of the Algebraic Riccati Equation