Publisher's Synopsis
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.;The purpose of the Short Course, which attracted approximately 140 participants, was to present a sample of the ways in which modern matrix theory is stimulated by its interplay with other subjects, such as combinatorics, probability theory, statistics, operator theory and control theory, algebraic coding theory, partial differential equations, and analytic function theory. Among the themes in this volume are the notion of majorization, the trend away from "basis-free" point of view, problem-dependent symmetries, and the synergy between matrix theory and systems theory.;The immense variety of tools and problems in this area illustrates one reason for using the term "matrix theory" or "matrix analysis" instead of "linear algebra"; a large portion of current work is neither primarily linear nor primarily algebraic in nature. The breadth of interest in this subject seems to point to future developments as fruitful and unexpected as in the past.
