Construction of Hyperplane, Supporting Hyperplane, and Separating Hyperplane on ℝ n and Its Application

Abstract

Abstract Hyperplane, supporting hyperplane and separating hyperplane have been defined well in inner product space. These definitions are expressed in very general concept of space, so in its understanding it requires understanding the specific inner product space. It is difficult, so in this paper the definitions will be explained in the ℝ n space or Euclidean space, beginning with constructing all possible hyperplanes of a given convex set. From all the hyperplane constructions, they will be classified as supporting hyperplane or separating hyperplane. This understanding will be generalized in the case of convex set with point and with other convex set. To clarify this discussion, it is completed with several examples of the construction of the hyperplane in ℝ n . In addition, this paper will give some examples of the application of hyperplane construction in ℝ n in computing the distance between point and a convex set. The application will also be further discussed in a more general problem, namely the distance between two disjoint convex sets.