Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Class of Parameter Dependent Commuting Matrices   We present a novel class of real symmetric matrices in arbitrary dimension
$d$, linearly dependent on a parameter $x$. The matrix elements satisfy a set
of nontrivial constraints that arise from asking for commutation of pairs of
such matrices for all $x$, and an intuitive sufficiency condition for the
solvability of certain linear equations that arise therefrom. This class of
matrices generically violate the Wigner von Neumann non crossing rule, and is
argued to be intimately connected with finite dimensional Hamiltonians of
quantum integrable systems.

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The categories of this paper are: hep-th
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The categories of this paper are: atom-ph
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The categories of this paper are: stat
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The categories of this paper are: plasm-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: physics
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The categories of this paper are: q-fin
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: quant-ph
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The categories of this paper are: nlin
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The categories of this paper are: gr-qc
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The categories of this paper are: q-alg
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The categories of this paper are: supr-con
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The categories of this paper are: mtrl-th