Page 10 - A Course in Linear Algebra with Applications

PREFACE TO THE FIRST EDITION

A rough and ready definition of linear algebra might be: that
part of algebra which is concerned with quantities of the first
degree. Thus, at the very simplest level, it involves the so-
lution of systems of linear equations, and in a real sense this
elementary problem underlies the whole subject. Of all the
branches of algebra, linear algebra is the one which has found
the widest range of applications. Indeed there are few areas
of the mathematical, physical and social sciences which have
not benefitted from its power and precision. For anyone work-
ing in these fields a thorough knowledge of linear algebra has
become an indispensable tool. A recent feature is the greater
mathematical sophistication of users of the subject, due in
part to the increasing use of algebra in the information sci-
ences. At any rate it is no longer enough simply to be able to
perform Gaussian elimination and deal with real vector spaces
of dimensions two and three.
The aim of this book is to give a comprehensive intro-
duction to the core areas of linear algebra, while at the same
time providing a selection of applications. We have taken the
point of view that it is better to consider a few quality applica-
tions in depth, rather than attempt the almost impossible task
of covering all conceivable applications that potential readers
might have in mind.
The reader is not assumed to have any previous knowl-
edge of linear algebra - though in practice many will - but
is expected to have at least the mathematical maturity of a
student who has completed the calculus sequence. In North
America such a student will probably be in the second or third
year of study.
The book begins with a thorough discussion of matrix
operations. It is perhaps unfashionable to precede systems
of linear equations by matrices, but I feel that the central

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