I've watched the 3blue1brown essence of Linear Algebra series which is great tbh, but I've been trying to get a grip on Linear Algebra as I never took it in my CS program and found this video the other day and at the section "Linear Algebra is more like programming" (and as the previous section is titled, "linear algebra is not like algebra"). I was astonished at how much sense at least a small part of this topic makes now to me. Can't wait to dive deeper. The part that stood out to me for those that don't want to watch an hour long video is where Charles Frye, the instructor, (who has a PhD in ML) said that matrices shapes are like programming's types (they are like a constraint on how they can be manipulated), that matrices themselves are like functions (they take some set of data and return another set), and that matrix operations are like function composition (they allow functions to be combined and sort of short circuited to get to an expected output.) Near the end of the video he says that these matrix operations or "function compositions" can be refactored by either breaking them down into their subsequent composite parts or by combining them together in a similar fashion as you would refactor code for clarity of intent, simplicity, efficiency, etc.
