What would you suggest as a complimentary resource to this?
Strang can be great as a first book. He focuses more on what rather than why, so if one wants to delve deeper, it needs to be supplemented by a few other books.
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.
That said, Jordan form is uglier than spectral decomposition, to my taste that is. Spectral decomposition so beautiful and neat.