An Exposition of Hadamard Matrices

Abstract

The purpose and aim of this paper will be to acquaint the reader with the development of these matrices and the methods used to determine their existence. The beginning section will consist of definitions which are intended to enable those with only a limited mathematical background to understand this exposition. The second section will be devoted to the work of R.E.A.C. Paley and John Williamson, attempting to explain their theorems and proofs, with the primary goal being the method of proof. Some of these proofs will be reproduced almost in their entirety. The proofs of other assertions may be complete1y omitted, mentioning only a general method of procedure or none at all. The third section will be a short summary. An extension of these matrices to three dimensions then concludes the paper.