The Coolness of EE 263: Linear Dynamical Systems

Hi Readers,

I am taking a break from the homework in one of my classes at Stanford, EE 263, titled "Linear Dynamical Systems." It is a heavily linear algebra based class. Ah heck, it's all linear algebra. This is my first ever linear algebra class that I've taken, and it is kicking my ass with gusto. In my undergrad, I tried 4 different times to take linear algebra, but each time I ended up dropping the class, because it was just SO DAMN BORING. But this class - wow! It is incredibly interesting, and super applicable too! Let me explain.

When I tell people about this class, the inevitable first question arises - "what is a linear dynamical system?" I'm not 100% sure, but the way I describe it, it's a system that somehow can be formed into the form of y = Ax. To put it in real world terms, it is a system A, which behaves with a linear fashion to input x, such that it can reliably produce output y.

It sounds pretty ridiculous when I first heard it. But it's absolutely unbelievable, the kinds of questions we have put this to use. A lot of systems in the real world are roughly linear, and this class teaches you many methods to resolve problems in real life. Our midterm questions were all applied linear algebra questions. For example, let's say you have an ecosystem where the animal populations were all in equilibrium, and you release some number of animal x into the ecosystem, and watch the fluctuations of all other animals. With linear systems, you can reverse the process. If you wanted animal x to increase by a certain number at a certain time, there are ways to reverse the equation so that you know exactly how many of each animal you need to release into the system at time zero in order to achieve your goal.

This class teaches you a lot of applications of this. The easy one is of course, if you are given the input x and system A, to find output y. Or, given a limited set of input and output, figure out what the system is, and use it to predict what the future outputs will be. Or, given what the output is and how the system behaves, how do you trace it back to the input?

I never really thought linear algebra could be fun. And to be fair, there are times during this class when I just want to bang my head against a wall and just turn in incomplete homeworks (because they are SO long!). However, I think it's fantastically useful, and I hope to be able to use such things to build models of systems in the future. This seems especially apt with medical imaging, since much of medical imaging is based upon the idea of model construction and optimization.

Anyways, it's late and I should go home to sleep. Just wanted to start blogging again - my blog has been so neglected, and I want to revive it.

Cheers,
FCDH