Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Repr\'esentations d\'eterminantales effectives des polyn\^omes
  univari\'es par les matrices fl\`eches   We first show the existence of an effective determinantal representation for
any univariate polynomial with real coefficients. Then, we more precisely
establish that any univariate polynomial with real coefficients has an
effective determinantal representation with signature (r+s,s) if and only if it
has at least r real roots with multiplicity. The effective determinantal
representations we construct used arrow matrices.

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The categories of this paper are: q-bio
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The categories of this paper are: supr-con
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
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The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-lat
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The categories of this paper are: q-fin
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The categories of this paper are: atom-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ph
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The categories of this paper are: nlin