This book provides a comprehensive treatment of the theory of matrix polynomials. By a matrix polynomial (sometimes known as a )-matrix) is
understood a polynomial of a complex variable with matrix coefficients.
Basic matrix theory (including the Jordan form, etc.) may be viewed as a
theory of matrix polynomials fA - A of first degree. The theory developed
here is a natural extension to polynomials of higher degrees, and forms an
important new part of linear algebra for which the main concepts and results
have been arrived at during the past five years. The material has important
applications in differential equations, boundary value problems, the Wiener-
Hopf technique, system theory, analysis of vibrations, network theory,
filtering of multiple time series, numerical analysis, and other areas. The
mathematical tools employed are accessible even for undergraduate students
who have studied matrix theory and complex analysis. Consequently, the
book will be useful to a wide audience of engineers, scientists, mathema-
ticians, and students working in the fields mentioned, and it is to this audience
that the work is addressed.