Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The generalized Levinger transformation   In this paper, we present new results relating the numerical range of a
matrix $A$ with generalized Levinger transformation
$\mathcal{L}(A,\alpha,\beta) = \alphaH_A +\betaS_A$, where $H_A$ and $S_A$, are
respectively the Hermitian and skew-hermitian parts of $A$. Using these
results, we derive expressions for eigenvalues and eigenvectors of the
perturbed matrix $A + \mathcal{L}(E,\alpha,\beta)$, for a fixed matrix $E$ and
$\alpha, \beta$ are real parameters.

1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
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The categories of this paper are: stat
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The categories of this paper are: supr-con
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The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn