Around and around the rugged rocks, the ragged rascal ran.
Monthly Archive for April, 2005
I finished my second talk, it didn’t go as well as the first one, I was much less prepared. Ah well, what to do.
Now all I have to do is one more short topic and I’m finished.
I’m doing Descartes’ Rule of Signs. I have a short proof to present taken from a paper in the American Mathematical Monthly 2004.
General proof of the spectral theorem.
Two steps.
- Show that there is a real eigenvalue for T.
- By iteration and the theorem I already proved, show that there is an orthonormal basis composed entirely of eigenvectors of T.
Part 1.
Use the Fundamental Theorem of Algebra. Play with complex numbers to show that a linear map with the same matrix has a “real” eigenvalue.
Part 2.
Use induction, etc.
I think I’ll post a LaTeX’ed pdf of this when I’m finished. Maths sucks in plain text.
Yesterday was so absurdly productive, I’m relaxing a little today.
I finished the talk in the morning, did the talk, then in the arvo I finished the proof preperation for the genearal proof for my next talk. Just got to write it up neatly and I’m done.
Been getting up early. Today 5am. Yesterday and Wednesday 4am. 5am is a little more sane. Been doing yoga and meditation, then pushups, shower, huge breakfast, coffee, off to uni.
Time to get to work now 
Proved the spectral theorem for dimensions 2 & 3 today. It went rather well, I was excellently prepared apparently, though I didn’t think that before I did it. I need to work on my presentation skills. I agree. I was mumbling and jittery. Maybe I’ll actually practice giving the talk before I have to do it next time.
Next week I prove the general case. Which is a little more involved than I thought.
I found this excellent website, it’s pretty much wikipedia, why didn’t I think of that before (then again I’d have been too confused if I found this before).
Answers.com
Finally went to my numerical analysis class. It’s not so bad, 1 week behind. Still doing Newton’s method.
Don’t you just love driving
