There are many good resources! A few, depending on your inclination:

- For intuition: https://www.youtube.com/watch?v=fNk_zzaMoSs

- For rigor: https://ocw.mit.edu/courses/18-06-linear-algebra-spring-2010...

- For code: https://codingthematrix.com/

- For numerical/algorithmic details: https://people.maths.ox.ac.uk/trefethen/text.html

Rigor and Strang are not two words I'd put in the same sentence. Neil Strickland's notes https://neilstrickland.github.io/linear_maths/ (for the matrix point of view) or Jim Hefferon's book https://joshua.smcvt.edu/linearalgebra/index.html (for a vector-spacey treatment) are what comes to my mind when I think "rigor" (along with all sorts of older textbooks like Hoffman/Kunze); Jean Gallier's long set of notes https://www.cis.upenn.edu/~jean/math-deep.pdf goes even further in that direction.

The cool thing about numerical linear algebra is, as far as numerical analysis is concerned, it's probably one of the most accessible fields to the would-be citizen scientist.

It's been a long time since I've taken linear algebra but if you can find an OCW course, or a really good book I'd start there. You'll want some rigor under your belt. Once you do that, any good numerical analysis text will usually cover the basics (you'll need them) before going into the fascinating world of algorithms as they relate to linear algebra.

Numerical Linear Algebra by Trefethen and Bau is the resource I've seen recommended most often. I've only read the first few chapters but they are good and useful.

head to ulaff.net, they have textbooks, a set of computer exercises, a code repository, youtube lectures, the whole nine yards really starting with linear algebra 101 and culminating with numerical linear algebra

their treatment of numerical linear algebra is not as comprehensive as say the one you'd find in Watkins' Fundamentals of Matrix Computations but it's free