Matric algebra is a mathematical abstraction underlying many seemingly
diverse theories. Thus bilinear and quadratic forms, linear associative
algebra (hypercomplex systems), linear homogeneous trans- formations and
linear vector functions are various manifestations of matric algebra.
Other branches of mathematics as number theory, differential and
integral equations, continued fractions, projective geometry etc. make
use of certain portions of this subject. Indeed, many of the fundamental
properties of matrices were first discovered in the notation of a
particular application, and not until much later re- cognized in their
generality. It was not possible within the scope of this book to give a
completely detailed account of matric theory, nor is it intended to make
it an authoritative history of the subject. It has been the desire of
the writer to point out the various directions in which the theory leads
so that the reader may in a general way see its extent. While some
attempt has been made to unify certain parts of the theory, in general
the material has been taken as it was found in the literature, the
topics discussed in detail being those in which extensive research has
taken place. For most of the important theorems a brief and elegant
proof has sooner or later been found. It is hoped that most of these
have been incorporated in the text, and that the reader will derive as
much plea- sure from reading them as did the writer.