An Intuitive Guide to Linear Algebra (2012)

I recently finished going through MIT OCW's linear algebra class from Gilbert Strang. Without the struggle of doing the assignments, reading the text, and watching the lectures, I don't think I would have ever learned the content. While content like this and that from 3blue1brown are commendable and useful, it simply would not have lodged the ideas into my head. Now that the ideas of things like vector spaces, norms, orthogonality, rank, basis, etc are nearly second nature, the concepts…

It seems like college Linear Algebra expeiences fall into one of two buckets: either you took a "Linear Algebra / Differential Equations" class where you learned no theory and saw a bunch of practical examples and did problem sets that were routinely north of 10 pages, OR you took a highly theoretical course where everything was far too abstract for your first year of college level of comprehension. I took the first route and retained none of the information, despite…

I would also add that one fundamental aspect of linear algebra (that no one ever taught me in a class) is that non-linear problems are almost never analytically solvable (e.g. e^x= y is easily solved through logarithms, but even solving xe^x=y requires Lambert’s W function iirc). Almost all interesting real world problems are non-linear to some extent, therefore, linear algebra is really the only tool we have to make progress on many difficult problems (e.g. through linear approximation and then…

As an electrical-engineer turned machine-learning-grad-student, linear transformations have been involved in most everything I do since my first year of undergrad. But all this time, I've done matrix multiplication the way I was taught in high school: "The (i,j) element of AB is what you get by walking right across the i'th row of A while you walk down the j'th column of B, taking the sum of products as you go." It works, but there's no connection between that…