Preprint A322/2004
On pairs of vectors achieving the maximal angle of a convex cone

Alberto Seeger | Iusem, Alfredo Noel

**Keywords: **
antipodal points | antipodal faces | convex cone | pointedness | maximal angle

In this paper we explore the concept of antipodality relative to a closed convex cone K in a finite dimensional vector space. The problem under consideration consists of finding a pair of unit vectors in K achieving the maximal possible angle. We mention also a few results on the attainability of critical angles. By way of application of the general theory, we briefly discuss the problem of estimating the radius of pointedness of a cone.