@ZachWeinersmith @lavi I think standard textbooks like Strang focus too much on row reduction as a building block and too little on the idea of a matrix as a transformation of space (which is the most intuitive starting point for me). I don't know of any textbook that does that but (if you'll forgive the plug) I wrote a long-from exploration of PCA that takes that perspective and touches on most aspects of concrete linear algebra https://peterbloem.nl/publications/unraveling-pca