On homework 9, all of this correct only if we assume that
V is actually a real vector space, so assume that.
(To get this to work for complex vector spaces, you have to take
conjugates, so that (u,v) = [u]T * (conjugate([v])).)
Also, after problem one, the italicized comment should be: (u,w) = u^T
G w.
And there's a typo in the word previous.