1. The section on matrices should start (not end) with the orthogonal length preserving co-ordinate transformation. It's the easiest geometry/trig connection, the elements can be worked out by hand, demonstrates unitary property, and makes a nice segue into inverse. 2. The section on linear system response could make a mention of Fourier series (even Fourier integral). 3. It's still a mystery to me why linear algebra is not taught using the Dirac notation.