Title: The Convexity of Quadratic Maps and the Controllability of Coupled Systems
Description: A quadratic form on $Rn$ is a map of the form $x mapsto x T M x$, where $M$ is a symmetric $n times n$ matrix. A emph{quadratic map} from $Rn$ to $Rm$ is a map, all $m$ of whose components are quadratic forms. One of the two central questions in this thesis is this: when is the image of a quadratic map $Q:Rn rightarrow Rm$ a convex subset of $Rm$?