In Section 4.2, read about dilation and contraction operators
(pp 181 - 182 including Tables 8-9).
In 4.2, read about compositions of linear transformations.
Note how composition of linear transformations corresponds to
matrix multiplication. Note that this provides another way to see
that matrix multiplication will not be commutative: it matters, in
general, which transformation one applies first.
In 5.3, read about how the Wronskian of a set of functions can
be used as one test for independence.