Up till now we have spoken about algebraic objects, usually matrices and vectors. But, at the beginning of this book (see Section 1.2) we gave examples of vectors such as force, velocity, acceleration, coming from physics. It’s clear that we’ve used the word
to mean at least two distinct things. But how can physical or geometric objects have the same name as purely algebraic ones? In this chapter we will study the
and we will discover an extraordinary activity of the mathematical arts: the construction of models not only of physical, biological and statistical objects but also of other mathematical objects. Said another way: mathematical entities, often created to be models of something else, can themselves be modeled inside mathematics.