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.