Determinants

Abstract

In this chapter we intend to address the second question raised in section 3.6; the idea is to associate with each square matrix a number, called its ‘determinant’, which will tell us whether or not the matrix is invertible. This topic may be approached in a number of ways, ranging from the informal to the elegant and sophisticated, and, as is common in this rich and varied world, none is ideal from every standpoint: difficult choices have to be made. We have chosen to reject the elegant modern approaches because of their level of abstraction, and to give a slightly dated treatment which is, nevertheless, rigorous enough for those demanding thoroughness.