I still don't get why Axler decided to discuss the Jordan normal form after already doing the spectral theorem, it's a bit like presenting Riemannian integration after Lebesgue.
For the long term his emphasis on operators is probably better as naturally transitions into functional analysis, but you can get a lot of stuff done without ever touching them.
For the long term his emphasis on operators is probably better as naturally transitions into functional analysis, but you can get a lot of stuff done without ever touching them.