ABSTRACT
Our aim in this chapter is to treat some elementary material about matrices from a somewhat more advanced viewpoint. We begin by giving formal definitions of matrices, ordered n-tuples, row vectors, and column vectors. We then give several equivalent formulations of the familiar matrix operations (addition, scalar multiplication, matrix multiplication, transpose, etc.) and derive their basic properties. We also discuss how to implement elementary row and column operations by multiplying a matrix on the left or right by certain “elementary matrices.”
