Recovery of minimal bases and minimal indices of rational matrices from Fiedler-like pencils

DOI10.1016/j.laa.2018.12.021zbMath1410.65113OpenAlexW2907379406WikidataQ128679442 ScholiaQ128679442MaRDI QIDQ1736230

Ranjan Kumar Das, Rafikul Alam

Publication date: 26 March 2019

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

Full work available at URL: https://doi.org/10.1016/j.laa.2018.12.021

zbMATH Keywords

system matrixlinearizationeigenvectorrational matrixminimal indicesmatrix polynomialFiedler pencilminimal basis

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 (5)

Block full rank linearizations of rational matrices ⋮ Local linearizations of rational matrices with application to rational approximations of nonlinear eigenvalue problems ⋮ Generalized Fiedler Pencils for Rational Matrix Functions ⋮ On minimal bases and indices of rational matrices and their linearizations ⋮ Structured strong linearizations of structured rational matrices

Cites Work

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• A permuted factors approach for the linearization of polynomial matrices
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• Fiedler Companion Linearizations and the Recovery of Minimal Indices
• Minimal Bases of Rational Vector Spaces, with Applications to Multivariable Linear Systems
• Properties of the system matrix of a generalized state-space system†
• Strong Linearizations of Rational Matrices
• A new family of companion forms of polynomial matrices
• Nonlinear eigenvalue problems: a challenge for modern eigenvalue methods
• Generalized Fiedler Pencils for Rational Matrix Functions
• Eigenvectors and minimal bases for some families of Fiedler-like linearizations

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