Matrix Multiplication

Abstract

The point of view adopted in this book is that the main subject of linear algebra is linear substitutions, that is, recipes for expressing one set of variables as sums of multiples of another set of variables. In the first five chapters, the multipliers of the linear substitutions will be taken to be integers. The substitutions are called “linear” because an expression which involves a sum of multiples of variables is called a homogeneous linear* polynomial, which is to say, a polynomial in which each term contains exactly one variable and that variable occurs to the first power.