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Fiedler Companion Linearizations and the Recovery of Minimal Indices
TLDR
A standard way of dealing with a matrix polynomial $P(\lambda)$ is to convert it into an equivalent matrix pencil—a process known as linearization. Expand
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Spectral equivalence of matrix polynomials and the index sum theorem
Abstract The concept of linearization is fundamental for theory, applications, and spectral computations related to matrix polynomials. However, recent research on several important classes ofExpand
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LINEARIZATIONS OF SINGULAR MATRIX POLYNOMIALS AND THE RECOVERY OF MINIMAL INDICES
A standard way of dealing with a regular matrix polynomial P (λ) is to convert it into an equivalent matrix pencil - a process known as linearization. Two vector spaces of pencils L1(P ) and L2(P )Expand
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Matrix Polynomials with Completely Prescribed Eigenstructure
TLDR
We present necessary and sufficient conditions for the existence of a matrix polynomial when its degree, its finite and infinite elementary divisors, and its left and right minimal indices are prescribed. Expand
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The solution of the equation XA + AXT = 0 and its application to the theory of orbits
Abstract describe how to find the general solution of the matrix equation XA + AX T = 0 , with A ∈ C n × n , which allows us to determine the dimension of its solution space. This result hasExpand
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New bounds for roots of polynomials based on Fiedler companion matrices
Abstract Several matrix norms of the classical Frobenius companion matrices of a monic polynomial p ( z ) have been used in the literature to obtain simple lower and upper bounds on the absoluteExpand
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First order spectral perturbation theory of square singular matrix pencils
Abstract Let H ( λ ) = A 0 + λ A 1 be a square singular matrix pencil, and let λ 0 ∈ C be an eventually multiple eigenvalue of H ( λ ) . It is known that arbitrarily small perturbations of H ( λ )Expand
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Fiedler companion linearizations for rectangular matrix polynomials
The development of new classes of linearizations of square matrix polynomials that generalize the classical first and second Frobenius companion forms has attracted much attention in the last decade.Expand
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Backward stability of polynomial root-finding using Fiedler companion matrices
Computing roots of scalar polynomials as the eigenvalues of Frobenius companion matrices using backward stable eigenvalue algorithms is a classical approach. The introduction of new families ofExpand
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Low Rank Perturbation of Weierstrass Structure
TLDR
We show that for most matrices $B_0 + \lambda_0 B_1$ with ${\rm rank} in the Weierstrass canonical form, there are Jordan blocks corresponding to the eigenvalue of the perturbed pencil $A_0+A_1+B_1$. Expand
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