Axler does limit itself to vector spaces over real and complex fields, though.
That‘s fine, but I would have appreciated notices, which proofs and theorems do not hold in the general case.
It‘s an exercise for the reader.
That‘s fine, but I would have appreciated notices, which proofs and theorems do not hold in the general case.
It‘s an exercise for the reader.
> This book usually develops linear algebra simultaneously for real and complex vector spaces by letting F denote either the real or the complex numbers. If you and your students prefer to think of F as an arbitrary field, then see the comments at the end of Section 1A. I prefer avoiding arbitrary fields at this level because they introduce extra abstraction without leading to any new linear algebra
TBH, I don’t think there are surprises in the “general case” (whatever that is… modules over a PID??) that you can’t see by understanding the real&complex situation.