Linear preservers of copositive and completely positive matrices

Abstract: The objective of this manuscript is to understand the structure of an invertible linear map on the space of real symmetric matrices $\mathcal{S}^n$ that leaves invariant the closed convex cones of copositive and completely positive matrices ($COP_n$ and $CP_n$). A description of an invertible linear map on $\mathcal{S}^2$ such that $L(CP_2) \subset CP_2$ is completely determined.