This volume contains the lecture notes prepared for the AMS Short Course
on Matrix Theory and Applications, held in Phoenix in January, 1989.
Matrix theory continues to enjoy a renaissance that has accelerated in
the past decade, in part because of stimulation from a variety of
applications and considerable interplay with other parts of mathematics.
In addition, the great increase in the number and vitality of
specialists in the field has dispelled the popular misconception that
the subject has been fully researched.