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.
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© 2009 Birkhäuser Boston
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Luong, B. (2009). Linear Algebra. In: Fourier Analysis on Finite Abelian Groups. Applied and Numerical Harmonic Analysis. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4916-6_2
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DOI: https://doi.org/10.1007/978-0-8176-4916-6_2
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Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-4915-9
Online ISBN: 978-0-8176-4916-6
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