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Vector Spaces of Linearizations for Matrix Polynomials
TLDR
We show how to simply construct two vector spaces of pencils that generalize the companion forms of $P$, and prove that almost all of these pencils are linearizations for $P$. Expand
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Structured Polynomial Eigenvalue Problems: Good Vibrations from Good Linearizations
TLDR
In this paper several useful classes of structured polynomials (e.g., palindromic, even, odd) are identified and the relationships between them explored. Expand
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ON THE SOLUTION OF PALINDROMIC EIGENVALUE PROBLEMS
A rational eigenvalue problem of the form 1 (A T + •A0 + • 2 A1)x = 0 arising in the vibration analysis of rail tracks under periodic excitation is investigated. This eigenvalue problem is a specialExpand
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Jordan structures of alternating matrix polynomials
Alternating matrix polynomials, that is, polynomials whose coefficients alternate between symmetric and skew-symmetric matrices, generalize the notions of even and odd scalar polynomials. WeExpand
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Smith Forms of Palindromic Matrix Polynomials
Many applications give rise to matrix polynomials whose coefficients have a kind of reversal symmetry, a structure we call palindromic. Several properties of scalar palindromic polynomials areExpand
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Eigenvalue perturbation theory of classes of structured matrices under generic structured rank one perturbations
Abstract udy the perturbation theory of structured matrices under structured rank one perturbations, and then focus on several classes of complex matrices. Generic Jordan structures of perturbedExpand
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Skew-symmetric matrix polynomials and their Smith forms
We characterize the Smith form of skew-symmetric matrix polynomials over an arbitrary field $\F$, showing that all elementary divisors occur with even multiplicity. Restricting the class ofExpand
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Numerical methods for palindromic eigenvalue problems: Computing the anti-triangular Schur form
TLDR
We present structure-preserving numerical methods for the eigenvalue problem of complex palindromic pencils using the anti-triangular Schur form. Expand
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Condensed Forms for Skew-Hamiltonian/Hamiltonian Pencils
  • C. Mehl
  • Mathematics, Computer Science
  • SIAM J. Matrix Anal. Appl.
  • 21 October 1999
TLDR
In this paper we consider real or complex skew-Hamiltonian/Hamiltonian pencils $\lambda S-H$, i.e., pencils where S is a skew- Hamiltonian and H is a Hamiltonian matrix. Expand
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