A good part of matrix theory is functional analytic in spirit. This
statement can be turned around. There are many problems in operator
theory, where most of the complexities and subtleties are present in the
finite-dimensional case. My purpose in writing this book is to present a
systematic treatment of methods that are useful in the study of such
problems. This book is intended for use as a text for upper division and
gradu- ate courses. Courses based on parts of the material have been
given by me at the Indian Statistical Institute and at the University of
Toronto (in collaboration with Chandler Davis). The book should also be
useful as a reference for research workers in linear algebra, operator
theory, mathe- matical physics and numerical analysis. A possible
subtitle of this book could be Matrix Inequalities. A reader who works
through the book should expect to become proficient in the art of
deriving such inequalities. Other authors have compared this art to that
of cutting diamonds. One first has to acquire hard tools and then learn
how to use them delicately. The reader is expected to be very thoroughly
familiar with basic lin- ear algebra. The standard texts
Finite-Dimensional Vector Spaces by P.R.