Linear Algebra class has apparently turned into “let’s see how many stupid math puns we can come up with in a 50-minute time period.” Including figuring out the plot to a movie about null spaces.
And then I come home and do this nonsense:
(Yes, I know that’s the symbol for the empty set. It needed something, okay? In the epic movie we’re planning, the empty set saves the day anyway, so there.)
I think I have an idea for my NaNoWriMo endeavors this year now.
Alright y’all, my “for fun” class has been decided!
It’s LINEAR ALGEBRA!
But Claudia, you say, you already have taken Linear Algebra!
Indeed! But here are some reasons why I want to take it again:
1. It’s IMPORTANT. And I’m about 99% sure I could get a lot more out of it now than when I took it back in 2009. Now that I know I want to go study multivariate statistics—probably SEM specifically—I need to know my linear algebra. I need to know it very well. I knew it decently when I took multivariate stats and SEM, but now that I know how it’s used in those types of analyses, if I go back and take Linear again, I think I’ll be able to better pick out the really important stuff. At least to a greater degree than I did before.
2. I’m also taking Numerical Linear Algebra this semester as well, which (surprise, surprise) has Linear Algebra as a prereq. Since it’s been so long since I’ve had the prereq, I figured a little in-semester refresher could only be a good thing.
3. Calculus, trigonometry, and geometry are my friends. Algebra and I still spread dirty rumors about one another and glare hatefully at each other whenever we pass. This needs to change.
4. It’s being taught by Dr. Abo, the professor I had for Discrete Math last semester. Dr. Abo is very intelligent, very awesome, and very good at teaching. He’s also hilarious at times.
Yeah so anyway.
The matrix of LINEAR ALGEBRA!!!
So someone asked the awesome dudes at Ask a Mathematician/Physicist why determinants of matrices are defined in the strange way they are. And one of the opening sentences of the Physicist’s response was:
“The determinant has a lot of tremendously useful properties, but it’s a weird operation. You start with a matrix, take one number from every column and multiply them together, then do that in every possible combination, and half of the time you subtract, and there doesn’t seem to be any rhyme or reason why.”
That needs to be a textbook definition somewhere.
Anyway. This was an especially interesting read for me, since we just learned about the role of the Jacobian matrix’s determinant when performing a change of variables for multiple integrals.
The Physicist has an excellent explanation of it (along with pictures!), but it basically comes down to the fact that the determinant of a 3 x 3 matrix, if we treat the columns of the matrix as vectors, is actually equal to the volume of the parallelepiped (coolest shape name or coolest shape name?) formed by the vectors. Think about if you have two vectors in the xy-plane. You can extend vectors out from each of the tails of the vectors so that you have a parallelogram like this:
Finding the determinant of the 2 x 2 matrix that describes those two vectors is the same as finding the area of the parallelogram formed by them. Add one more dimension and you get a parallelepiped for your shape and a volume for your determinant.
This has a buttload of applications—like I said, when performing a change of variables when doing multiple integration, but also for finding eigenvalues/eigenvectors and determining whether a set of vectors are linearly independent or not.
I was actually planning on making this a longer blog with an actual calculus application, but a) formatting that would take like 80 years for me and I’ve actually got to study sometime tonight and b) I’ve fallen into the “polar coordinates” article on Wiki and I don’t think I’ll be getting out anytime soon. THEY MAKE ME HAPPY, OKAY?!
As much as I hated finding eigenvalues and eigenvectors (which was a lot), this article’s actually very interesting. Probably because some of this stuff is relevant to factor analysis, which is sexiness in statistics form.
That is all.
Today’s song: Animal by Miike Snow
SO CLOSE. I was SO CLOSE to getting another 4.0 this semester.
Because I’m stupid.
At least 3.98 is still above the summa cum laude cutoff.
Also, can you make me good at math? ‘Cause I’ve got my Linear Algebra final in less than three hours.
Last night I had this dream I was stuck in a 3×3 matrix and was subtracted to zero when they reduced it to echelon form.
It was scary as hell. Mainly because it was a DREAM ABOUT ALGEBRA.
I want to shoot myself.
Because I’m a stupid, worthless, hopeless piece of crap who is afraid of math, I decided to drop Linear Algebra.
Go ahead and laugh, I deserve it.
Haha, hooray for more school. Abnormal Psychology looks fun and interesting. Linear Algebra, on the other hand, does not.
I get it, I just don’t like it. And I’d forgotten how much I loathed the setup of math books.