Non-Commutative Partial Matrix Convexity

Damon M. Hay, J. William Helton, Adrian Lim +1

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…