After taking a couple classes on programming (I know, CS isn't just programming) and an upper division intro to combinatorics, I'd like to get more into the area of discrete mathematics. I hope to pursue a PhD at some point, but I'm not sure how strong of a school I can get into since currently...
Homework Statement
We have a finite group ##G## and a homomorphism ##\rho: G \rightarrow \mathbb{GL}_n(\mathbb{R})## where ##n## is a positve integer. I need to show that there's an ##n\times n## positive definite symmetric matrix that satisfies ##\rho(g)^tA\rho(g)=A## for all ##g \in G##...
NEVER MIND!
Sorry, it's late, but I totally forgot the definition of $<g>$ when the group operation is addition. I computed it for that, and my results matched. I guess my problem is not with the computation, but rather when I need to take a break and go to sleep. I'm not sure I can...
Hello. So today in class, we talked a bit about <g> as the set of all integer powers of g. Made enough sense. Then we did some examples in \mathbb{Z} / 7\mathbb{Z}, and I got a bit lost. I think this is more due to the fact that perhaps I don't quite grasp \bmod{n} as an equivalence class. So I...