Determinants part II

The determinant of a matrix can be thought of as a function which associates a real number with every square matrix. In this chapter, we will see how this association is made. We will also see the kind of information about a matrix its determinant can give us. We begin by introducing some terminology and notation which will be used from this point on. All the matrices we deal with in this chapter, unless stated otherwise, will be square matrices. One approach to de.ne determinants is to use a recursive de.nition, that is de.ne the determinant of an nn matrix in terms of determinants of n??1n??1 matrices. In turn, these determinants of n ?? 1  n ?? 1 matrices will be de.ned in terms of determinants of n ?? 2  n ?? 2 matrices. And so on. Of course, we do need an absolute de.nition for 2  2 matrices.