[dxbydt]

> Maybe my understanding is all wrong, feel free to correct me, as my understanding on this subject is entirely self-taught.

I wouldn't say it is all wrong. Just that the stuff you are talking about is a very tiny fraction of LA. I took a graduate class in LA, based on Strang's book. I have the book right here in front of me. So the stuff you allude to, i.e. rotation matrix, reflection matrix & projection matrix, is on p130 of Chapter 2. We got to that in the 1st month of the semester, & it got about 1 hour of classtime total. That's it. An LA class is like 4 months, or 50 hours. If the point of LA to derive those matrices so one can do 3D computer graphics with scaling, rotation & projection ? No, that stuff is too basic. We got 1 homework problem on that, that's it.

The stuff that most of the class struggled with ( & still struggle with, because Strang goes over it rather quickly in his book), is function spaces ( chapter 3, p182), Gram Schmidt for functions ( p184), FFTs, (p195), fibonacci & lucas numbers (p255), the whole stability of differential equations chapter ( he gives these hard and fast rules like a Differential Equation is stable if trace is negative & determinant is positive, but its not too clear why. ), quadratic forms & minimum principles - that whole 6th chapter glosses over too much material imo.

Overall, Strang's book is a solid A+ on how to get stuff done, but maybe a B- on why stuff works the way it works. Like, why should I find Rayleigh quotient if I want to minimize one quadratic divided by another ? Strang just says, do it & you'll get the minimum. How to find a quadratic over [-1,1] that is the least distance away from a cubic in that same space ? Again, Strang gives a method but the why part of it is quite mysterious.

[pengaru]

Thanks for writing this. I intend to pick up a physical copy of Strang's book as it's been repeatedly mentioned in a positive light on HN.

So does LA get substantially more involved than just lots of multiplications and additions or is it always at the end of the day still just bags of floats getting multiplied and summed? Is it just a fantastic rabbit hole describing what values you put where in those bags of numbers?