Read or begin reading 4.2: Linear Transformations from
Rn to R m.
For purposes of this chapter, such a transformation is
simply a function from R n to R m
that is given in the form of multiplication by an m x n
matrix.
The examples in this section are mainly geometric ones from
R 2 to R 2 or R
3 to R 3.
The key thing to get out of this section is a familiarity
with how these various operations (such as reflections,
rotations, projections, magnifications or contractions) can be
characterized via matrix multiplication.
These operations/transformations will be used as examples
later in the course.
Perhaps skim or begin reading 4.3: Properties of Linear
Transformations from Rn to R
m.
For now your goal with this section is just to get the
flavor of what's discussed there.
Read 5.1: Real Vector Spaces.
For now, your goal should be to understand the examples
that are given and how they are (or are not) vector spaces
according to the definition given in class and on p204.
Soon we will discuss the additional properties of scalar
multiplication that are described in Theorem 5.1.1. If you've
read that material you'll be ahead of the game.