So...Finals are Over.

Exams are now over, and now I am off-campus, waiting until my work term starts. Life feels empty. I realize that Christmas/Newtonmas/whatever people celebrate these days is either soon or recently over, but still...

Anyway, linear algebra final was yesterday; it was terrible. But fun. Except for the obligatory "solve the eigenvalue problem for this matrix" (and use the information to do stuff about orthonormality). Two particular problems got stuck in my head:

1. Let T be a diagonalizable linear map from V to V. a) If T has n distinct eigenvalues, show that V has finitely many T-invariant subspaces. b) If T has less than n distinct eigenvalues, show that V has infinitely many T-invariant subspaces.
2. Suppose an n*n complex matrix A is such that A^m tends to matrix B (in the sense that each entry of A^m tends to the corresponding entry in B). Show that a) each eigenvalue &lambda of A is such that |&lambda| < 1 or &lambda = 1. b) B must have 0 or 1 as an eigenvalue. c) if &mu is an eigenvalue of B, &mu is either 0 or 1.

Question 2 is much easier than question 1, in my opinion. But dealing with complex entries gets a bit messy and I think I didn't explain my solution very well *sigh*. Question 1 I didn't really do at all. The professor said two lines of the solution afterwards, and I was sad.

Maybe this winter break is a good time to post all those things I said I would post but didn't. But then, my notes are currently in storage right now...we'll see.

Linear algebra aside, I also have unofficial marks for most of my courses, except for organic and linear algebra (obviously). (Begin whine) While I am anxious for the marks that I don't have yet, those that I see already make me depressed; I barely passed^* some of my chemistry courses *sigh*. To think that I was (relatively) pleased with my chemistry marks last year! CS wasn't that great either, but then, I didn't love CS in the first place. Amazingly, I did better in statistics than in calculus. This does not say anything positive about my calculus mark.

I fear to see my mark in organic (might even fail the course); there certainly will be no perfects this term :(

To avoid having people throw things at me, I shall refrain from posting my marks.
(end whine)

All I can do is to hope that taking less courses in the summer will help my marks improve. Besides, there's thermodynamics (officially this time) in the summer. Thermodynamics is good.

For what I will be planning to do over the work term, well, I'll post that as "New Year's Resolutions".

Meanwhile, it is probably a good time to read some of my new books. In the end, I got Griffiths, and Liboff, for quantum mechanics, because everything else was sold out or otherwise not available. Kutzelnigg is not available in English as far as I know. I also got a classical mechanics textbook for the special relativity chapter. Yes, it was expensive. Very. But the purchase made me less depressed than I would probably be after organic final.

^* Well, ok. Using my definition of passing, which is different from the one at the Registrar. But still.