August 4, 2010
After the last post on the real spectral theorem, I don’t have too much more to do in linear algebra. I think this is around all I need to study for my placement exams as far as linear algebra is concerned — and so, for now, this is where I’ll probably end. I’ve yet to post an example of using the spectral theorems, and I may post something about using complex vector spaces (since I found a bit about how to define them, etc, etc.) but for the most part, I’m not gonna write too much more about linear algebra.
On the other hand, I haven’t really even begun to study multivariable, so I’ve begun by putting up some random tidbits of information. The reason for this is twofold: because lengthy and well-laid-out texts for multivariable calculus are available (for example, I use Stewart‘s calculus now, but there are many others.) and, in addition, because these concepts as a whole take a ton of time and patience to develop. I have neither. Consequently, I will be posting about little things that I find interesting or, perhaps, tricky. Anything that takes me a little while to "figure out" from Stewart’s text, I will post on here.
What about my claim (a while ago!) that we’re going to use linear algebra to study groups? This is still true. I don’t have my representation theory book anymore, but it’s being sent to me eventually; when I have it, I can begin writing about it.
Last, all I want is to you guys to have fun! So if you have a topic you want me to explore, tell me! Please. I like hearing from you guys!