I am a PhD student in physics and I would definitely say that linear algebra is more important.

What should I learn if I'm interested in learning linear algebra?

3Blue1Brown has a great video intro series on the topic. https://www.youtube.com/channel/UCYO_jab_esuFRV4b17AJtAw/vid...

terrific! thank you.

I made notes some time ago that cover the linear algebra needed for Quantum Mechanics in some details and then go on to introduce basic QM at the end:

https://graybits.biz/notes/quantum_mechanics/preface

cool stuff. thank you.

Your question is rather tautological... You can pick a text book or even an online tutorial.

Understanding diagonalization (and more generally, spectral theory), scalar products, and norms would be a great start. Then you can pick any quantum information textbook.

algebra?

But what should I learn if I'm interested in learning algebra?

N.B. My maturity level is normally only a half step above the average 12-year-old. I can play this game all day ;)

hey! you got me ;)

My PhD is in biophysics. The Hamiltonion is a functional, pretty much all QM is application of Hamiltonians. I know both LA and FA; LA is basically introduction to FA.

It really depends on the area. For quantum computing and quantum info theory it seems that mostly it is just linear algebra. The functional stuff is left for the really really clever people only (not me btw!)

The way you describe it sounds analogous to computers: like saying "you only need to know C, not transistor physics, to program a computer". You can code on an existing machine, port your code to a new machine, but you'll never invent a new machine or architecture.

I think most would say that functional analysis is a generalization of linear algebra and that you absolutely need your linear algebra first. (Functional analysis is often thought of as infinite dimensional linear algebra.) Moreover, (finite dimensional) linear algebra is sufficient for learning theoretical quantum computing where there is a finite number of states.