Since its inception by Perron and Frobenius, the theory of non-negative
matrices has developed enormously and is now being used and extended in
applied fields of study as diverse as probability theory, numerical analysis,
demography, mathematical economics, and dynamic programming, while its
development is still proceeding rapidly as a branch of pure mathematics in
its own right. While there are books which cover this or that aspect of the
theory, it is nevertheless not uncommon for workers in one or another branch
of its development to be unaware of what is known in other branches, even
though there is often formal overlap. One of the purposes of this book is to
relate several aspects of the theory, insofar as this is possible.
The author hopes that the book will be useful to mathematicians; but in
particular to the workers in applied fields, so the mathematics has been kept
as simple as could be managed. The mathematical requisites for reading it
are: some knowledge of real-variable theory, and matrix theory; and a little
knowledge of complex-variable; the emphasis is on real-variable methods.
(There is only one part of the book, the second part of §5.5, which is of rather
specialist interest, and requires deeper knowledge.) Appendices provide brief
expositions of those areas of mathematics needed which may be less gen-
generally known to the average reader.