In this chapter we are going to start looking at the idea of a vector and the ultimate goal of this chapter will be to define something called Euclidean n-space.  In this chapter we’ll be looking at some very specific examples of vectors so we can build up some of the ideas that surround them.  We will reserve general vectors for the next chapter.

We will also be taking a quick look at the topic of linear transformations.  Linear transformations are a very important idea in the study of Linear Algebra.

Here is a listing of the topics in this chapter.

Vectors  In this section we’ll introduce vectors in 2-space and 3-space as well as some of the important ideas about them.

Dot Product & Cross Product  Here we’ll look at the dot product and the cross product, two important products for vectors.  We’ll also take a look at an application of the dot product.

Euclidean n-Space  We’ll introduce the idea of Euclidean n-space in this section and extend many of the ideas of the previous two sections.

Linear Transformations  In this section we’ll introduce the topic of linear transformations and look at many of their properties.

Examples of Linear Transformations  We’ll take a look at quite a few examples of linear transformations in this section.