Non-Commutative Partial Matrix Convexity
| dc.creator | Hay, Damon M. | |
| dc.creator | Helton, J. William | |
| dc.creator | Lim, Adrian | |
| dc.creator | McCullough, Scott | |
| dc.date | 2008-04-03 | |
| dc.date.accessioned | 2026-07-07T09:30:24Z | |
| dc.date.available | 2026-07-07T09:30:24Z | |
| dc.description | 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 $p = L + Λ^T Λ,$ where $L$ has degree at most one in $x$ and $Λ$ is a (column) vector which is linear in $x,$ so that $Λ^TΛ$ 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. | |
| dc.description | 24 pages | |
| dc.identifier | https://arxiv.org/abs/0804.0633 | |
| dc.identifier | http://arxiv.org/abs/0804.0633 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/158114 | |
| dc.subject | Functional Analysis | |
| dc.subject | Optimization and Control | |
| dc.title | Non-Commutative Partial Matrix Convexity | |
| dc.type | text |