The main topics are:
- vector spaces and matrices
- matrix inverses
- orthogonality
(that is chapters 15-19 of the lecture notes)

[determinants are NOT part of test4]

Here is a list of exercises to help you prepare:

If you have not done these yet, exercises from the Easter non-DGD session: all from the notes, 18.1 b,d - 18.2 b,d,h - 19.1 b,d - 19.3 b,d - 19.4 d - 19.6 b,d,f,h

From the lecture notes (only * exercises come with a solution):
16.2, 16.4

From old tests:
Q3 -
Q3, Q4, Q5*, Q6b -
* here best approximation just means "the projection on U"

Note: some exercises (19.1 for instance) ask you the "Fourier coefficient" of some vector in an OG basis. This just means find the coordinates of a vector in an orthogonal basis. (see p205 of the notes)