For a given subset of Euclidean space, we define the support function of this set. This function will be the largest inner product of a given point from the given subset. The support function will always be a convex function. We prove that it is homogeneous of degree one and that the support function of the Minkowski sum is the sum of the support functions. Finally, we prove tha the support function of the unit ball is the standard Euclidean norm.
#mikethemathematician, #mikedabkowski, #profdabkowski, #convexanalysis, #machinelearning
