Date

5-1-2015

Document Type

Honors Project

First Advisor

Hydorn, Debra

Department Chair or Program Director

Helmstutler, Randall

Degree Name

Bachelor of Science

Major or Concentration

Mathematics

Department or Program

Mathematics

Abstract

In this paper, the eigenvectors of interpoint distance matrices will be discussed. When plotted against each other, the eigenvectors of the distance matrix of evenly spaced points in one dimension produce some interesting patterns. An explanation and description of the patterns will be discussed. After examining many aspects of the general Euclidean interpoint distance matrix of order N, D, as well as characteristics of the eigenvectors themselves,some conclusions can be made. Furthermore, research revealed a similarity between our matrices, D, and the Discrete Cosine Transform Matrix, DCT-2. This research led to additional conclusion about our matrices D and allowed for a classification of the patterns within the graphs of the eigenvectors.

Language

English

Included in

Mathematics Commons

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