Nate Eldredge

Abstract The classical Fourier transform is, in essence, a way to take data and extract components (in the form of complex exponentials) which are invariant under cyclic shifts. We consider a case in which the components must instead be invariant under automorphisms of a binary tree. We present a technique by which a slightly relaxed form of the generalized Fourier transform in this case can eventually be computed using only simple tools from linear algebra, which has possible advantages in computational efficiency.

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The Senior Thesis Program Department of Mathematics Harvey Mudd College	Nate Eldredge Harvey Mudd College Mathematics 2003 Primary research interests: Representation Theory, Spectral Analysis, Combinatorics, Computational Algebra Other mathematical interests: Real Analysis, Topology, Graph Theory Starting in the fall of 2003, I will be a graduate student in the Department of Mathematics at the University of California, San Diego in beautiful La Jolla.
	Senior Thesis An Eigenspace Approach to Isotypic Projections for Data on Binary Trees Advisor: Michael Orrison Second Reader: Shahriar Shahriari
	Abstract The classical Fourier transform is, in essence, a way to take data and extract components (in the form of complex exponentials) which are invariant under cyclic shifts. We consider a case in which the components must instead be invariant under automorphisms of a binary tree. We present a technique by which a slightly relaxed form of the generalized Fourier transform in this case can eventually be computed using only simple tools from linear algebra, which has possible advantages in computational efficiency. Download: PDF

Nate Eldredge

Senior ThesisAn Eigenspace Approach to Isotypic Projections for Data on Binary Trees

Senior Thesis
An Eigenspace Approach to Isotypic Projections for Data on Binary Trees