I went through EE and CS. EE we started using matrices exactly how you describe it: here’s a system of linear equations, here’s how you write them in matrix form, here’s how you invert them to solve the original system. Turn the crank, answer pops out. I had my trusty HP49G, and I could solve linear systems all day.
Then in CS I took a computer graphics course and it was rotation and translation matrices all day every day.
Then there was a digital communications course where we touched on orthogonal basis functions, and some matrix voodoo related to that and how to get orthogonal vectors out of the mess.
And then finally I took the required CS linear algebra course offered by the math department, where we started from scratch. Here’s a vector (psh, I know vectors!), here’s a vector space (hmmm this is new), and building the rest of it up from there. I really wish that had come earlier on, but I was very very happy to finally have a bit of a theoretical understanding of how these tools I’d been using actually worked.
I feel like my university only taught calculation, not theory, when it came to linear algebra. It’s like the equivalent of a “12 hacks to rotate a matrix” article. The theoretical books I find however give no explanation for the definitions etc, ie, WHY are the dot/cross products defined the way they are. It’s as though they feel matrixes are natural phenomenon that you should just memorize the properties of, which is also nonsense.
The entire field is defined by such terrible books. I’d love to be wrong though if somebody has a recommendation
Then in CS I took a computer graphics course and it was rotation and translation matrices all day every day.
Then there was a digital communications course where we touched on orthogonal basis functions, and some matrix voodoo related to that and how to get orthogonal vectors out of the mess.
And then finally I took the required CS linear algebra course offered by the math department, where we started from scratch. Here’s a vector (psh, I know vectors!), here’s a vector space (hmmm this is new), and building the rest of it up from there. I really wish that had come earlier on, but I was very very happy to finally have a bit of a theoretical understanding of how these tools I’d been using actually worked.