Chapter 4: Vector Spaces
The entire last chapter led up to defining vector spaces. Now we will see how some vector spaces can be subsumed by other vector spaces. We'll revisit linear combinations to talk about linear independence. We will also learn new ways to define vector spaces with just a small set of vectors. Finally, while we used the word dimension previously to describe a vector space, we will attain a mathematical definition for it in this chapter.
In this chapter, we are going to cover the following main topics:
- Subspaces
- Linear independence
- Span
- Basis
- Dimension
Subspaces
Let's say you have a set, U, of vectors and it is a subset of a set, V, of vectors (U ⊆ V). This situation is shown in the following diagram:
Figure 4.1 – ...
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