An Eigenspace Approach to Isotypic Projections for Data on Binary Trees

Nathaniel Eldredge

Senior Thesis
Department of Mathematics
Harvey Mudd College

Advisor: Michael Orrison, Department of Mathematics, Harvey Mudd College
Second Reader: Shahriar Shahriari, Department of Mathematics, Pomona College


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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