I just... Here's the deal. Most good math is elegant, it has a beauty about it. And as a programmer, good code has the same "feel." But when I took Andrew Ng's class, gradient descent felt... not beautiful at all... and just based on that beauty-seeking intuition, there MUST be a more elegant way to get directly at the inverse of a matrix (assuming it exists and is possible) than all of these... complicated expensive workarounds. And the pot at the end of that rainbow is you get the EXACT value that gradient descent is wasting all this time trying to snowboard down N-dimensional space to get to!

I know I may be asking to make what may be a fundamentally-hard problem, easy... I'm just saying that I don't get the same, eh, "buzz" I get when I see a really cool solution for something (which I've often gotten from math, physics, programming, etc.). This is very hard to explain as it's probably irrational and thus I can't make a strong rational argument for it lol (admittedly!)

I really love linear algebra, btw, so this should be right up my alley.