ABSTRACT

Linear algebra is the study of linear maps, the vector-valued functions u = L(x) of a vector variable x, having the linearity property: L(ax + by) = aL(x)+bL(y), where a, b are scalars. Such functions can be scaled and added, provided their domains and codomains are the same. We can even multiply or compose two such functions, provided the range of the first is a subset of the domain of the second. We shall see in Chapter 4 that when the domains and codomains are “finite dimensional vector spaces,” the algebra of such functions is basically the matrix algebra which we study in this chapter.