Polyconvexity is an important concept in the analysis of energies related to elasticity. A function \(W :\mathbb {R}^{d\times d} \rightarrow \mathbb {R}\) is called polyconvex if it can be written as a convex function in the minors of the argument. We show that for isotropic functions it suffices to consider diagonal matrices. For \(d=3\) , this leads to a dimension reduction for the convex representative of W from \(\mathbb {R}^{19}\) to \(\mathbb {R}^7\) . Moreover, we present a new result for the polyconvexity of functions formulated in the principal invariant of the left or right stretch tensor.
