FWIW, I was told that matrices are linear maps pretty early on in my education. Are there any college level linear algebra / matrix calculations courses that don't tell students about that?
When I went through university the standard set of courses was a Calculus course that was mostly about derivatives, a second one that was mostly about integrals, a third Calculus course that was about multi-variable Calculus. That third course necessarily had to teach matrices, and taught it as rote calculations. There was a follow-up differential equations course which refreshed people's memories of matrices..as a rote calculation.
It was done this way because the multi-variable Calculus course was a prerequisite for a lot of physics+engineering courses. So a lot of students wanted to take that sequence. Differential equations were a prerequisite for some other advanced courses. Linear algebra was pretty much just for math majors.
It's possible if you learned matrices outside the context of a linear algebra class that you might be mystified about what's actually happening.
I took Linear Algebra the same semester I took Computer Graphics, which worked out really well for me - the first half of LA taught me everything I needed to know about transformation matrices, and the second half of CG covered 3D graphics in OpenGL. The first half of CG was all 2D graphics stuff, and the second half of LA was about eigenvectors/values - I've forgotten everything from that part of the class.
> FWIW, I was told that matrices are linear maps pretty early on in my education. Are there any college level linear algebra / matrix calculations courses that don't tell students about that?
I know they taught us about matrices in high school, but I don't recall them talking about any applications at all. I think the topic was pretty drained of context, just rote application of the rules for add/subtract/multiply/etc.
Sure they'll tell you that in passing, but won't really explain what that actually means. Certainly Linear Algebra 1 at college was a lot of apply this method to this object (that we'll call a matrix) to calculate this thing called a determinant. Don't worry about what it is or what it represents, just check if it's zero or not. If it's not zero apply this other method to calculate its inverse. Repeat.
Same here in the UK - a big chunk of the Oxford School Mathematics Project O-level syllabus in the early 80s comprised the various transformations and the matrix operations needed to create them.
I find Strang's text to be unnecessarily tedious. Both of Lang's LA textbooks (Intro to LA, and LA) both take linear maps as the core point of the text.
When I went through university the standard set of courses was a Calculus course that was mostly about derivatives, a second one that was mostly about integrals, a third Calculus course that was about multi-variable Calculus. That third course necessarily had to teach matrices, and taught it as rote calculations. There was a follow-up differential equations course which refreshed people's memories of matrices..as a rote calculation.
It was done this way because the multi-variable Calculus course was a prerequisite for a lot of physics+engineering courses. So a lot of students wanted to take that sequence. Differential equations were a prerequisite for some other advanced courses. Linear algebra was pretty much just for math majors.