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MiS Preprint
69/2003
Rank-One Convex Hulls in $\Bbb R^{2\times 2}$
László Székelyhidi
Abstract
We study the rank-one convex hull of compact sets $K\subset\R^{2\times 2}$. We show that if $K$ contains no two matrices whose difference has rank one, and if $K$ contains no four matrices forming a $T_4$ configuration, then the rank-one convex hull $K^{rc}$ is equal to $K$. Furthermore, we give a simple numerical criterion for testing for $T_4$ configurations.