I continued with linear algebra. I went through some of Terence Tao’s linear algebra notes. Especially weeks 3, 4, 5, 6. I have gone through similar material in Axler’s book and other places, which is why I was able to go through the material relatively quickly. I mostly read the notes, but worked out some of the proofs before reading/did some of the exercises.

It’s interesting for me to see how different authors cover the same material (I also enjoyed doing this with real analysis). For instance, Tao gives up on doing determinants completely rigorously, saying we would need more advanced machinery to understand it properly. Tao also does fun one-dimensional unit conversion (length, currency) and chemistry (converting molecules to atoms, etc.) examples. I also hadn’t seen the shear operation explained in terms of a parallelogram’s area before (i.e. the shear operation changes neither the base nor the height of a parallelogram, so does not change the determinant).

I still feel like linear algebra is a jumble of facts. At the same time, I feel like there is a way to organize everything neatly (I think this table is a start), and that’s one of the things motivating me right now.