In broad terms, vectors are things you can add and linear functions are functions of vectors that respect vector addition. The goal of this text is to teach you to organize information about vector spaces in a way that makes
problems involving linear functions of many variables easy. (Or at least tractable.) To get a feel for the general idea of organizing information, of vectors, and of linear functions this chapter has brief sections on each. We start
here in hopes of putting students in the right mindset for the odyssey that follows; the latter chapters cover the same material at a slower pace. Please be prepared to change the way you think about some familiar mathematical
objects and keep a pencil and piece of paper handy. But lets think carefully; what is the left hand side of this equation doing? Functions and equations are different mathematical objects so why is the equal sign necessary?