LADR is probably the best linear algebra book around. It's a bit of a shame that the "marketing" mostly involves the fact that it does not use determinants.
The last edition also contains chapters on stuff like dual spaces and quotient spaces, which are important yet very often missing in other textbooks.
That being said, his reliance on C/R in about half the book could be a problem for people with CS background. Like, what if I want to compute determinants of linear maps which are over Z_2? There are also no chapters on number wrangling (like the gaussian elimination and friends), which is a big plus in my view but possibly a problem for others.