I've also gone over those lectures a couple of times. I'm not even sure why I started watching them, since I knew absolutely nothing about linear dynamical systems before hand, but it really changed my life! It taught me techniques that I now use all the time, and I think are very neglected within my field (data analysis/forecasting).
If your not familiar with it, it's an extremely versatile framework for modeling and analysis of all kinds of systems. It will give you new insights into linear algebra, time series analysis, stochastic models, Fourier analysis, Laplace transforms, and many other areas.
He's a brilliant (and enthusiastic) teacher, and he has lots of resources on line, including a text-book length exercise-set which I've printed out and had bound because it is so awesome.
