I self-taught myself linear algebra from Strang's book, combined with his lectures (on youtube). I wouldn't say that his approach is proof-heavy at all. Further

I self-taught myself linear algebra from Strang's book, combined with his lectures (on youtube). I wouldn't say that his approach is proof-heavy at all. Furthermore, the proofs in LA are rather easy and mechanical, compared to other areas of maths (and also, you can just skip them when reading).