Pointedness of images of convex cones under linear maps

Let K ⊂ R n be a convex cone, and let L : R n → R m a linear map. We show some results regarding ker L and the pointedness of L ( K ) . In particular, we present an equivalence between the pointedness of L ( K ) and a decomposition of K into a sum involving ker L and a pointed, convex cone. Further, L ( K ) is a pointed, convex cone if, and only if, K ∩ ker L is a face of K . As an application, we present some results on the stability of pointedness of L ( K ) under small perturbations of L .