Semiconvexity of invariant functions of rectangular matrices

The paper deals with the semiconvexity properties (i.e., the rank 1 convexity, quasiconvexity, polyconvexity, and convexity) of rotationally invariant functions f of matrices. For the invariance with respect to the proper orthogonal group and the invariance with respect to the full orthogonal group coincide. With each invariant f one can associate a fully invariant function of a square matrix of type where It is shown that f has the semi convexity of a given type if and only if has the semiconvexity of that type. Consequently the semiconvex hulls of f can be determined by evaluating the corresponding hulls of and then extending them to matrices by rotational invariance. Received: 10 October 2001 / Accepted: 23 January 2002 // Published online: 6 August 2002 RID="*" ID="*" This research was supported by Grant 201/00/1516 of the Czech Republic.