Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-Commutative Partial Matrix Convexity   Let $p$ be a polynomial in the non-commuting variables
$(a,x)=(a_1,...,a_{g_a},x_1,...,x_{g_x})$. If $p$ is convex in the variables
$x$, then $p$ has degree two in $x$ and moreover, $p$ has the form $p = L +
\Lambda ^T \Lambda,$ where $L$ has degree at most one in $x$ and $\Lambda$ is a
(column) vector which is linear in $x,$ so that $\Lambda^T\Lambda$ is a both
sum of squares and homogeneous of degree two. Of course the converse is true
also. Further results involving various convexity hypotheses on the $x$ and $a$
variables separately are presented.

8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con