Rank-one convex hulls in $${\mathbb{R}^{2\times2}}$$

Abstract

We study the rank-one convex hull of compact sets \(K\subset\mathbb{R}^{2\times2}\). We show that if K contains no two matrices whose difference has rank one, and if K contains no four matrices forming a T4 configuration, then the rank-one convex hull Krc is equal to K. Furthermore, we give a simple numerical criterion for testing for T4 configurations.