## On the non-homogeneity of completely positive cones

### Abstract:

For a closed cone $\C$ in $\rn$, the completely positive cone of $\C$ is the convex cone $\K$ in $\sn$ generated by $\{uu^T:u\in \C\}$. In this article, we describe some properties of $\K$ and, in particular, investigate when (or whether) $\K$ can be self-dual, irreducible, or homogeneous.

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