Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On a Class of Matrix Pencils and $\ell$-ifications Equivalent to a Given
  Matrix Polynomial   A new class of linearizations and $\ell$-ifications for $m\times m$ matrix
polynomials $P(x)$ of degree $n$ is proposed. The $\ell$-ifications in this
class have the form $A(x) = D(x) + (e\otimes I_m) W(x)$ where $D$ is a block
diagonal matrix polynomial with blocks $B_i(x)$ of size $m$, $W$ is an $m\times
qm$ matrix polynomial and $e=(1,\ldots,1)^t\in\mathbb C^q$, for a suitable
integer $q$. The blocks $B_i(x)$ can be chosen a priori, subjected to some
restrictions. Under additional assumptions on the blocks $B_i(x)$ the matrix
polynomial $A(x)$ is a strong $\ell$-ification, i.e., the reversed polynomial
of $A(x)$ defined by $A^\#(x) := x^{\mathrm{deg} A(x)} A(x^{-1})$ is an
$\ell$-ification of $P^\#(x)$. The eigenvectors of the matrix polynomials
$P(x)$ and $A(x)$ are related by means of explicit formulas. Some practical
examples of $\ell$-ifications are provided. A strategy for choosing $B_i(x)$ in
such a way that $A(x)$ is a well conditioned linearization of $P(x)$ is
proposed. Some numerical experiments that validate the theoretical results are
reported

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The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
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The categories of this paper are: stat
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The categories of this paper are: acc-phys
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The categories of this paper are: q-fin
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The categories of this paper are: q-alg
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The categories of this paper are: bayes-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
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The categories of this paper are: q-bio
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The categories of this paper are: eess