Polyconvex function

In mathematics, the notion of polyconvexity is a generalization of the notion of convexity for functions defined on spaces of matrices. Let "M""m"×"n"("K") denote the space of all "m" × "n" matrices over the field "K", which may be either the real numbers R, or the complex numbers C. A function "f" : "M""m"×"n"("K") → R ∪ {±∞} is said to be polyconvex if
can be written as a convex function of the "p" × "p" subdeterminants of "A", for 1 ≤ "p" ≤ min{"m", "n"}.
Polyconvexity is a weaker property than convexity. For example, the function "f" given by
is polyconvex but not convex.