Linear algebra done right

The most useful consensus was about sequencing. People who had taught from Strang, Axler, and similar texts kept saying the same thing: Strang or Lay work better for a first pass, especially for self-learners, engineers, and anyone coming from 3Blue1Brown wanting intuition tied to computation. Axler shines after that, when you already know what matrices do and want the abstract picture that connects linear algebra to more advanced math. Several readers said Axler felt clearer than Strang to their brains, but even fans described it as aimed at honors students or a second course rather than the default beginner path. The determinant fight was the other recurring theme, but the comments did not really vindicate one camp over the other. They clarified the tradeoff. Axler’s long-running hostility to determinants is a pedagogical choice, not a universally accepted correction to the field. Supporters said determinants are often taught as a bag of formulas before students know what problem they solve. Critics said avoiding them can become a distracting crusade, especially because geometric ideas like signed volume and invertibility are exactly what make the concept click for many learners. The practical reading is that the title is marketing and pedagogy, not a final verdict on how linear algebra ought to be taught. Once you strip away the book-title skirmish, the stronger point was broader: linear algebra is not one subject with one natural introduction. Some people need it as computation on matrices. Others need it as geometry, transformations, proof training, or preparation for Fourier analysis and other abstract settings. That is why the recommendation list sprawled. People kept pointing newcomers toward different books based on whether they wanted ML and graphics foundations, rigorous proof practice, coding-heavy exercises, or a gentler bridge into the subject. The page ended up being less a defense of Axler than a map of when to use it.