## 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

### 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.