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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.