A 2020 Vision of Linear Algebra
It's ridiculous how much random college-level linear algebra textbook material I stared at before things clicked in the course of just jumping in and exploring 3D graphics and writing my own 3D vector, matrix multiplication and 3D transform headers and using them in making some games in plain C.<p>At some point it's like "Wait, is linear algebra really just about heaps of multiplication and addition?  Like every dimension gets multiplied by values for every dimension, and values 0 and 1 are way more interesting than I previously appreciated.  That funny identity matrix with the diagonal 1s in a sea of 0s, that's just an orthonormal basis where each corresponding dimension's axis is getting 100% of the multiplication like a noop.  This is ridiculously simple yet unlocks an entire new world of understanding, why the hell couldn't my textbooks explain it in these terms on page 1? FML"<p>I'm still a noob when it comes to linear algebra and 3D stuff, but it feels like all the textbooks in the world couldn't have taught me what some hands-on 3D graphics programming impressed upon me rather quickly.  Maybe my understanding is all wrong, feel free to correct me, as my understanding on this subject is entirely self-taught.