Handbook of Linear Algebra, 2nd Edition

Chapter 84

Matrix Groups

Peter J. Cameron

Queen Mary, University of London

The topics of this chapter and the next (on group representations) are closely related. Here we consider some particular groups that arise most naturally as matrix groups or quotients of them, and special properties of matrix groups that are not shared by arbitrary groups. In representation theory, we consider what we learn about a group by considering all its homomorphisms to matrix groups. In this chapter we discuss properties of specific matrix groups, especially the general linear group (consisting of all invertible matrices of given size over a given field) and the related “classical groups.” Most group theoretic terminology is standard and can be found in any textbook ...