doing 2nd year LA right now (as a mature age) have done calc before but this is probably the hardest maths ive been exposed to so far. so many new and abstract concepts to get my head around and try to visualise. and sometimes you just cant visualise it, its abstract. you just have to trust the development of an idea and go "yeah, it generalises i guess"
like i always thought of inner products as just dot products but its a whole theory on its own, and cayley hamilton theorm, just been exposed to that but no idea how its useful yet
I consider myself an expert in linear algebra and I still find Cayley-Hamilton perplexing. Like it's clearly true but the proofs are unsatisfying It feels like there is an algebraic system that would make it obvious but hasn't been discovered yet (or at least I'm not aware of it).
like i always thought of inner products as just dot products but its a whole theory on its own, and cayley hamilton theorm, just been exposed to that but no idea how its useful yet