Non-visual Linear Algebra

I have been studying the basics of linear algebra over the last four weeks. I used two different resources: I started with the famed MIT OpenCourseWare course by Gilbert Strang. I gave up on it by lecture 4 and moved to mathacademy.com, a platform that focuses on drilling active math knowledge. At the same time, I rewatched 3Blue1Brown’s Essence of Linear Algebra series. I had watched that series once before studying any linear algebra. The first pass before I had done any serious linear algebra was a waste of time. Without the concrete experience of operations like finding eigenvalues or eigenvectors, the beautiful diagrams don’t mean much.

At the same time, the opposite is also true. A few times, while doing the many exercises on Math Academy, I wondered what beautiful things in engineering or science I would eventually be able to do with this. The course is great for getting a first handle on linear algebra without giving up, but it doesn’t give you the excitement and flavour of what you can do with it.

I have had to find this for myself. And there is a very real lack of such descriptions. I don’t really understand why we start with the abstract concept — “here is what diagonalization means, let’s do some diagonalizations” — instead of starting with the differential equations you can solve with it, and then dropping a level to show the mechanics.

I believe in hard work and perseverance. I believe it needs to be trained and does not come naturally. But life is not just one problem after another. There are truly wonderful things you can do with technical knowledge.