Duality of matrix pencils, Wong chains and linearizations

DOI10.1016/j.laa.2015.01.015zbMath1308.15009OpenAlexW2048100122MaRDI QIDQ2261572

Federico Poloni, Vanni Noferini

Publication date: 6 March 2015

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

Full work available at URL: https://doi.org/10.1016/j.laa.2015.01.015

zbMATH Keywords

linearizationKronecker canonical formmatrix polynomialmatrix pencilFiedler pencilsingular pencilpencil dualityWong chain

Mathematics Subject Classification ID

Eigenvalues, singular values, and eigenvectors (15A18) Matrix pencils (15A22)

Related Items (11)

On the exponential generating function for non-backtracking walks ⋮ The limit empirical spectral distribution of complex matrix polynomials ⋮ The limit empirical spectral distribution of Gaussian monic complex matrix polynomials ⋮ The Deformed Graph Laplacian and Its Applications to Network Centrality Analysis ⋮ Chebyshev rootfinding via computing eigenvalues of colleague matrices: when is it stable? ⋮ Matrices in companion rings, Smith forms, and the homology of 3-dimensional Brieskorn manifolds ⋮ On the nearest stable \(2\times 2\) matrix, dedicated to Prof. Sze-Bi Hsu in appreciation of his inspiring ideas ⋮ On the stability of computing polynomial roots via confederate linearizations ⋮ Fiedler-comrade and Fiedler--Chebyshev pencils ⋮ Root polynomials and their role in the theory of matrix polynomials ⋮ On computing root polynomials and minimal bases of matrix pencils

Uses Software

• NLEVP

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Spectral equivalence of matrix polynomials and the index sum theorem
• The quasi-Weierstrass form for regular matrix pencils
• Fiedler companion linearizations for rectangular matrix polynomials
• Using permuted graph bases in \(\mathcal{H}_\infty\) control
• New reachability and observability tests for positive linear discrete-time systems
• A permuted factors approach for the linearization of polynomial matrices
• AB-algorithm and its modifications for the spectral problems of linear pencils of matrices
• General theory of regular matrix polynomials and band Toeplitz operators
• The eigenvalue problem \(\lambda Tx+Sx\)
• An inverse free parallel spectral divide and conquer algorithm for nonsymmetric eigenproblems
• Methods and algorithms of solving spectral problems for polynomial and rational matrices
• A structure-preserving doubling algorithm for continuous-time algebraic Riccati equations
• Canonical forms for Hamiltonian and symplectic matrices and pencils
• Fast linear algebra is stable
• An arithmetic for matrix pencils: theory and new algorithms
• The Quadratic Eigenvalue Problem
• The Quasi-Kronecker Form For Matrix Pencils
• Fiedler Companion Linearizations and the Recovery of Minimal Indices
• Smith forms of palindromic matrix polynomials
• The behavior of the complete eigenstructure of a polynomial matrix under a generic rational transformation
• NLEVP
• Minimal Bases of Rational Vector Spaces, with Applications to Multivariable Linear Systems
• A new family of companion forms of polynomial matrices
• Using Algebraic Geometry
• Doubling Algorithms with Permuted Lagrangian Graph Bases
• A Deflation Approach for Large-Scale Lur'e Equations
• Addition to “The Quasi-Kronecker Form for Matrix Pencils
• Matrix Polynomials
• Vector Spaces of Linearizations for Matrix Polynomials

This page was built for publication: Duality of matrix pencils, Wong chains and linearizations