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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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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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The Conditioning of Linearizations of Matrix Polynomials
TLDR
The standard way of solving the polynomial eigenvalue problem of degree $m$ in $n\times n$ matrices is to “linearize” to a pencil in vector space $\mathbb{DL}(P)$ of pencils recently identified and studied by Mackey and Mehrmann. Expand
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Symmetric Linearizations for Matrix Polynomials
TLDR
A standard way of treating the polynomial eigenvalue problem $P(\lambda)x = 0$ is to convert it into an equivalent matrix pencil—a process known as linearization. Expand
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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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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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Structured Factorizations in Scalar Product Spaces
TLDR
We study the structure in eigenvalues, eigenvectors, and singular values that persists across a wide range of scalar products of a scalar product when the product is factored. Expand
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Definite Matrix Polynomials and their Linearization by Definite Pencils
TLDR
We extend the definition of hyperbolic matrix polynomial in a way that relaxes the requirement of definiteness of the leading coefficient matrix, yielding what we call definite polynomials. Expand
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