additional notes (redux)

[nibot]

1. I found the key, lying in the grass. We've regained ground thought lost to the entropy.

2. whitewhale went and saw Mr. Mandelbrot, for whom is named this thing, one of the most magnificent and wonderous objects in all of Mathematics:
   

3. I essentially aced my continuum mechanics midterm. I say "essentially" because I received only 40% credit for one of the questions despite having a manifestly correct response. Among my errors were referring to the existence of complex numbers and committing the cultural faux pas of using dirac notation instead of undersquiggles. Clearly I should have listened to squarkz. I have written for redress of these grievences.
   

4. My advisor complimented me on my photo of the goodman street yard, which I have on the wall here. I ventured an explanation, that it was taken from the roof of my "other apartment." He became very confused, possibly even agitated, about why I would have such a thing as the loft. The best answer I can give is, "for fun," which was apparently not satisfactory.
   

Comments

[wealhtheow.livejournal.com]

That's one badass fucking fractal (http://www.jonathancoulton.com/lyrics/mandelbrot-set).

[hukuma.livejournal.com]

Cool, I got two links to jonathancoulton in one day!

[nibot.livejournal.com]

http://en.wikipedia.org/wiki/Dirac_notation

It's pretty silly actually. The thing like |v〉 is a vector and the thing like 〈v| is... a covarient tensor? 〈x|y〉 is the inner product of x and y, and |x〉〈y| is the outer product, ie a linear operator, i.e. a once-covarient once-contravarient tensor (??). The great thing is that the entire system is predicated on a pun. The inner product 〈x|y〉 is called a bracket, so the 〈x| gets called a bra and the |y〉 gets called a ket. We talk about eigenkets about as much as we would eigenvectors, but thankfully never eigenbras.

I guess x⊗y is a more conventional notation, but then you don't know what part is covariant or which part is contravarient, eh? I think in other areas of physics we might write that, in coordinate form, as something like x^μ_ν.

[nibot.livejournal.com]

make that x^μy_ν.

[onhava.livejournal.com]

Are you sure you had a complete correct response on that midterm? The matrix {{a,0,0},{0,a,0},{0,0,c}} that you find doesn't seem to be the only response, if I understand the question correctly; what about {{0,a,0},{-a,0,0},{0,0,c}}?

[nibot.livejournal.com]

That matrix does work, but part of the statement of the problem (not included in the above attachment, sorry) was that we were looking only for symmetric matrices. My general result (the one involving lambdas) gives that result for λ₁=λ₂ and λ₁, λ₂ ∈ I.

[onhava.livejournal.com]

Ah, symmetric. I see. Did you complain?

success!

[nibot.livejournal.com]

Yes! And I got my points:

Tobin,

I think you are right. I apologize.
Setting the 12 and 21 entries to real values
obviously gives that 11=22. I have changed your
test grade to 30/30.

JCL

[squarkz.livejournal.com]

3. the correct vector notation on an exam is whatever the professor has been using for the last few weeks. (i am not personally a fan of the undersquiggles.)

4. where else would you keep the mistress?