Sib comments are suggesting textbooks (good ones at least, IMO), but FWIW, if I were trying to give someone a 1 or 2 hour intro to LA, it would be:
- Strang's 4 subspaces: https://web.mit.edu/18.06/www/Essays/newpaper_ver3.pdf , and just enough supporting material to understand that at a basic level, and hopefully finishing up with the SVD, which to me is basically a summary of LA in one equation.
- A quick look at the eigenvalue problem, Ax = 𝛌x, with the key note that hey, in the vast majority of cases, Ax does not equal a scaled version of x (it took me way too long to realize that's what we were doing here when I was first learning LA). <roll tacoma narrows bridge tape here>
- Strang's 4 subspaces: https://web.mit.edu/18.06/www/Essays/newpaper_ver3.pdf , and just enough supporting material to understand that at a basic level, and hopefully finishing up with the SVD, which to me is basically a summary of LA in one equation.
- A quick look at the eigenvalue problem, Ax = 𝛌x, with the key note that hey, in the vast majority of cases, Ax does not equal a scaled version of x (it took me way too long to realize that's what we were doing here when I was first learning LA). <roll tacoma narrows bridge tape here>