CR Drost (kentox) wrote,
CR Drost
kentox

I've made friends with another NL/US dual citizen -- a cute lesbian geek named Josine/Josina. We've got a rather shared history, surprisingly, so I feel obligated to help her along with her confusions. She went to Smith; I went to Cornell -- so of course, I'm understanding a bajillion things that she's missing.

She learned Quantum Mechanics without Linear Algebra, dudes. Quantum mechanics is linear algebra (in funny hats). But she'd seen vectors and dot products and determinants and the like before; she just hadn't had a formal course in them.

So I took it upon myself to teach her a nearly four-hour crash course in linear algebra, which took the second half of the day.

The first two hours were devoted to some review of
(1) What linearity is [ f(x + y) = f(x) + f(y), f(kx) = k f(x). ]
(2) Why every linear function can be characterized as a matrix.
(3) How to do matrix multiplication.
(4) Coordinate systems.
(5) A little bit of matrix inversion (especially the 2x2 case), but not the explicit case of solving linear systems.
(6) Questions, some problems.

Coffee break! I illustrated Scott Aaronson's "Proof by Pizza" and explained calculus in under a minute to a crowd of undergrad physics majors. I got a round of applause.

The second two hours covered:
(1) Eigenvectors. ("Making f(x + y) = f(x) + f(y) even simpler.")
(2) Eigenvalues.
(3) Eigenvalues in Quantum Mechanics.
(4) Matrices as seen from their diagonalizing coordinates.
(5) The determinant of a diagonal matrix, and the physical interpretation of it.
(6) Determinants in general, det(AB) = det(A) det(B), det(AT) = det(A).
(7) Why, if M v = 0 for a nontrivial v, then det M = 0. (just diagonalize M).
(8) How to actually find eigenvalues [ derivation of det(M − λI) = 0. ]
(9) Finding an eigenvector with a given eigenvalue.

It sounds like more, but I didn't have to talk at great length about how to do determinants with Josina -- she understood from the start. She just didn't know why they were important and what they physically meant, so I tried to show her.

All in all, I thought it was a pretty good crash course.
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