so. I hate Matrices. I know i linked to something "matrix-y" below, but that was a gesture suffused with irony. i hate them because of a class i took at MIT, 18.06, aka linear algebra (SHOUT OUT: Ethan). this class was supposedly easy, but i found it to be mind bogglingly difficult. i'll never forget walking into the class the first day and the [visiting] professor was like "ok, everyone. turn your text books over. everything you need to know about linear algebra is captured in this picture on the back." the picture on the back? it was two overlapping rectangles, one what more rhombus-y. actually, less rhombus-y and more like a 1yr old child was trying to draw two overlapping squares. this is like version 7.0 of the image:
needless to say, the "drawing" meant nothing to me then, and nothing to me now, and subsequent tries meet the goals (see below) of the class were unsuccessful.
GOALS FOR 18.06 as per the syllabus:
1. Solving Ax = b for square systems by elimination (pivots, multipliers, back substitution, invertibility of A, factorization into A = LU)
2. Complete solution to Ax = b (column space containing b, rank of A, nullspace of A and special solutions to Ax = 0 from row reduced R)
3. Basis and dimension (bases for the four fundamental subspaces)
4. Least squares solutions (closest line by understanding projections)
5. Orthogonalization by Gram-Schmidt (factorization into A = QR)
6. Properties of determinants (leading to the cofactor formula and the sum over all n! permutations, applications to inv(A) and volume)
7. Eigenvalues and eigenvectors (diagonalizing A, computing powers A^k and matrix exponentials to solve difference and differential equations)
8. Symmetric matrices and positive definite matrices (real eigenvalues and orthogonal eigenvectors, tests for x'Ax > 0, applications)
9. Linear transformations and change of basis (connected to the Singular Value Decomposition -- orthonormal bases that diagonalize A)
10. Linear algebra in engineering (graphs and networks, Markov matrices, Fourier matrix, Fast Fourier Transform, linear programming)
I got a D.
ANYWAY. i mention this because for the longest time, i refused to see the movie "The Matrix." and while i enjoyed the first one when i finally saw it, i continued to have reservations based solely on the title. and then the second one BLEW, and i almost can't believe there's a third. so this quote from a NYTimes review made me inordinately happy:
"Reloaded" was certainly a lumpy, gaseous treatise of a movie...Mr. Reeves, perhaps worried that he was showing too much range, has purged himself of all expression apart from a worried frown and a sorrowful grimace." it got a D too!
the moral: matrix-related things ain't no fun, and like it or not: we are not living in an orthogonal world, and i am definitely not an orthogonal girl.