Rotationally Invariant Rank 1 Convex Functions

Let f be a function on the set M ⁿ xn of all n by n real matrices. If f is rotationally invariant with respect to the proper orthogonal group, it has a representation tilde f through the signed singular values of the matrix argument ?∈ M^nxn. Necessary and sufficient conditions are given for the rank 1 convexity of f in terms of tilde f . Accepted 20 December 2000. Online Publication 18 May, 2001.