Linear Algebra

Abstract

The FT is a linear operator defined, for our purposes, on finitedimensional inner product spaces. Given a finite Abelian group G, we will define the FT (in Chapter 4) to be a linear operator on a finite-dimensional inner product space associated with G. More generally, in this chapter, we define an association of sets with inner product spaces. We also define dual bases and a special type of linear operator, i.e., a type of operator that carries orthonormal bases to orthonormal bases. These operators are then formulated in terms of orthonormal bases and the dual of these bases.