ABSTRACT
The term matrix was introduced by James Joseph Sylvester (1814-1897) in 1850, and the first paper on matrix algebra was published by Arthur Cayley (1821-1895) in 1858 [24]. Although the primary goal of this chapter is to describe the basics of matrix arithmetic and matrix algebra, towards the end we begin matrix theory proper with an introduction to diagonalization, an idea of fundamental importance in mathematics. This chapter, together with Chapters 9 and 10, forms the first step in the subject known as linear algebra, the importance of which is hard to overemphasize.
8.1 MATRIX ARITHMETIC A matrix1 is a rectangular array of numbers. In this book, you can usually assume that the numbers are real but on occasion complex numbers, modular arithmetic and even polynomials will be used.
