Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Short Proof of the Symmetric Determinantal Representation of
  Polynomials   We provide a short proof of the theorem that every real multivariate
polynomial has a symmetric determinantal representation, which was first proved
in J. W. Helton, S. A. McCullough, and V. Vinnikov, Noncommutative convexity
arises from linear matrix inequalities, J. Funct. Anal. 240 (2006), 105-191. We
then provide an example using our approach and extend our results from the real
field $\mathbb{R}$ to an arbitrary field $\mathbb{F}$ different from
characteristic $2$. The new approach we take is only based on elementary
results from the theory of determinants, the theory of Schur complements, and
basic properties of polynomials.

15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio