I finally finished the Linear Algebra block this week, which I’m very happy about. It’s not that I didn’t enjoy it, but I feel like I’ve been working through it for years, not months!
The final unit was about eigenvectors, with a big section about using eigenvectors to recognise the various kinds of non-degenerate conics and quadric surfaces from their equations. It was a bit taxing, but I really enjoyed that section. I find it weirdly satisfying to go through the big drawn-out process of writing the equation in matrix form, diagonalising the matrix, changing coordinate systems, etc, because when you’ve finished all the detective work you get to shout “It’s an elliptic paraboloid!” or whatever it turns out to be. (I promise I won’t actually shout this in the exam.)
I think quadric surfaces are just lovely to look at and think about, quite apart from the fun of identifying them via eigenvectors. I especially like hyperboloids, like the one pictured above, and hyperbolic paraboloids like the ones pictured to the right. Apparently Pringles crisps are also in the shape of hyperbolic paraboloids, so they’re definitely my favourite quadrics! If I was a tutor, I’d make sure to bring several tubes of Pringles to the Linear Algebra day school – I’m sure being bribed with crisps would make even the toughest bit of matrix algebra more pleasant!
Pringles: a legitimate part of any linear algebra study session.