The Structure and Properties of a Class of Affine Subspaces and Applications in Mechatronics Science

Abstract

Information science focuses on understanding problems from the perspective of the stakeholders involved and then applying information and other technologies as needed. We show that every affine subspace is the orthogonal direct sum of at most three purely non-reducing subspaces. This result is obtained through considering the basicquestion as to when the orthogonal complement of an afffine subspace in another one is still affine subspace. Motivated by the fundamental question as to whethor every affine subspace is singly-generated wavelet frame, we prove that every affine sub -space can be decomposed into the direct sum of a singly-generated afffine subspace.