Recovery of eigenvectors of rational matrix functions from Fiedler-like linearizations

DOI10.1016/j.laa.2016.09.009zbMath1352.65115OpenAlexW2520136921MaRDI QIDQ501256

Rafikul Alam, Namita Behera

Publication date: 29 December 2016

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

Full work available at URL: https://doi.org/10.1016/j.laa.2016.09.009

zbMATH Keywords

eigenvaluelinearizationminimal realizationeigenvectorzerosmatrix polynomialmatrix pencilpolesFiedler pencilrational matrix function

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Eigenvalues, singular values, and eigenvectors (15A18) Hermitian, skew-Hermitian, and related matrices (15B57) Numerical computation of matrix norms, conditioning, scaling (65F35)

Related Items (9)

Generalized Fiedler pencils with repetition for rational matrix functions ⋮ Automatic recovery of eigenvectors and minimal bases of matrix polynomials from generalized Fiedler pencils with repetition ⋮ Block full rank linearizations of rational matrices ⋮ Generalized Fiedler Pencils for Rational Matrix Functions ⋮ Recovery of minimal bases and minimal indices of rational matrices from Fiedler-like pencils ⋮ On minimal bases and indices of rational matrices and their linearizations ⋮ Van Dooren's Index Sum Theorem and Rational Matrices with Prescribed Structural Data ⋮ Fiedler Linearizations for Higher Order State-Space Systems ⋮ Structured strong linearizations of structured rational matrices

Cites Work

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• Fiedler Companion Linearizations and the Recovery of Minimal Indices
• A new family of companion forms of polynomial matrices
• Nonlinear eigenvalue problems: a challenge for modern eigenvalue methods
• Vector Spaces of Linearizations for Matrix Polynomials

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