LINEAR MAPPINGS PRESERVING THE COPOSITIVE CONE

摘要

Let S-n be the set of all n-by-n symmetric real matrices, and let C-n be the copositive cone, that is, the set of all matrices a is an element of S-n that fulfill the condition u(inverted perpendicular) au >= 0 for all n-vectors u with nonnegative entries. We prove that a linear mapping phi : S-n -> S-n satisfies phi(C-n) = C-n if and only if