Let S be a convex set in En and S a convex set in Em. Suppose T is an m n

matrix that establishes a one-to-one correspondence between S and S , i.e., for

every s S there is s S such that Ts = s, and for every s S there is a

single s S such that Ts = s. Show that there is a one-to-one correspondence

between extreme points of S and S .