Schur complements and state space realizations

DOI10.1016/j.laa.2004.10.027zbMath1083.47016OpenAlexW2037259482MaRDI QIDQ1772731

Marinus A. Kaashoek, Israel Gohberg, André C. M. Ran, Harm Bart

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.2004.10.027

zbMATH Keywords

equivalenceSchur complementtransfer functionfactorizationextensionrealization

Mathematics Subject Classification ID

Factorization of matrices (15A23) 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) Dilations, extensions, compressions of linear operators (47A20) Operator means involving linear operators, shorted linear operators, etc. (47A64)

Related Items

On equivalence and linearization of operator matrix functions with unbounded entries, Equivalence after extension and Schur coupling do not coincide on essentially incomparable Banach spaces, Equivalence after extension and Schur coupling for relatively regular operators, On realization of left and right products of rational functions, Equivalence after extension and matricial coupling coincide with Schur coupling, on separable Hilbert spaces, Lipschitz properties of structure preserving matrix perturbations, Schur coupling and related equivalence relations for operators on a Hilbert space, On the Schur complement form of the Dirichlet-to-Neumann operator, On the Reduction of Linear Systems Related to Boundary Value Problems, Equivalence after extension and Schur coupling coincide for inessential operators, Singular Sylvester equation in Banach spaces and its applications: Fredholm theory approach, Stabilisation of matrix polynomials, On Certain Positivity Classes of Operators, An eigenvalue multiplicity formula for the Schur complement of a \(3\times3\) block operator matrix, Diffraction from Polygonal-conical Screens, an Operator Approach, Equivalence after extension for compact operators on Banach spaces

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