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May
1
accepted Why do the characters of an abelian group form a group?
Apr
25
comment Limit of recursive sequence $n^2q_n=1+(n-1)^2q_{n-1}+2(n-2)q_{n-2}$
@almagest is correct, if there is a converging solution then $q_n \sim q_{n-1} \sim q_{n-2}$ so to solve that equation^ could would give the value of $q_n$ if it converges to anything. In this case $q_n = \frac{1}{3}$ is the only valid solution, so if it does converge to something, it'll be that.
Apr
25
comment Why do the characters of an abelian group form a group?
goblin, this is something I didn't know, but I think @user1952009 makes it clear since $\frac{1}{\chi} = \chi^*$ (because the traces have to be elements in the complex unit circle). I guess that answers the question.
Apr
25
comment Why do the characters of an abelian group form a group?
hmm... the original comment appears to have disappeared.
Apr
25
comment Why do the characters of an abelian group form a group?
Then what exactly does the author mean when he writes: " let $\hat{G}$ be the set of irreducible characters of $G$. If $\chi_1, \chi_2$ belong to $\hat{G}$, the same is true of their product $\chi_1 \chi_2$ "? I know that the character of the tensor product of two representations, is the product of their characters. Does that mean there is a different representation, whose character is the product of the two original characters, that is not the tensor product of the two original representations?
Apr
25
asked Why do the characters of an abelian group form a group?
Apr
25
awarded  Custodian
Apr
25
comment representation theory and schur's lemma
how does "commutativity [imply] that there exists a simultaneous eigenvector"? The best I can get is that if $AB = BA$ then for an eigenvectors $u| Au = u$ that $Bu$ is necessarily an eigenvector, (and by symmetry you can similarly find eigenvectors of $B$), but it's not clear why these are shared.
Apr
22
comment UpMultiset Combination-choose 3
If the authors are still alive, i'd consider sending them an email. Perhaps I don't (nor do the other responders) understand exactly what they mean by how many ways can a selection of 5 be made. Either you'll have a found a bug and they'll be appreciative, or at least they'll know how to make the question clearer in later editions.
Apr
22
comment UpMultiset Combination-choose 3
Please take a look at the post now, and let me know if any parts aren't clear
Apr
22
revised UpMultiset Combination-choose 3
added 703 characters in body
Apr
22
comment UpMultiset Combination-choose 3
Why is subtracting the two an answer? $$ \begin{pmatrix} 9 \\ 4 \end{pmatrix}$$ measures the number of ways to pick 4 items from the 9 that aren't the same.$$ \begin{pmatrix} 12 \\ 5 \end{pmatrix}$$ measures every way to pick 5 items from 12. If we subtract the two, we end up with "Every way to pick 5 items from 12, except those cases where we pick exactly one of the items that is in the group of 3". This doesn't make any sense
Apr
22
comment UpMultiset Combination-choose 3
Proof of what I've written? Which aspect particularly? The general formula or the example, or both?
Apr
20
comment Evaluate this infinite product: $\prod_{n=3}^{\infty} \left(\;1-\frac{4}{n^2}\;\right)$
It's a way to approximate the factorial function. Sometime's it's useful when you want to get an asymptotic approximation of the factorial without being super accurate (such as in a limit). The problem is your multiplication meant that even the smaller parts that I was neglecting by the approximation affected the answer, and hence I made a mistake by using it. If you're curious you can read more about it here: en.wikipedia.org/wiki/Stirling%27s_approximation
Apr
20
revised Evaluate this infinite product: $\prod_{n=3}^{\infty} \left(\;1-\frac{4}{n^2}\;\right)$
added 508 characters in body
Apr
20
comment Evaluate this infinite product: $\prod_{n=3}^{\infty} \left(\;1-\frac{4}{n^2}\;\right)$
Oh I see where it was too rough
Apr
20
comment Evaluate this infinite product: $\prod_{n=3}^{\infty} \left(\;1-\frac{4}{n^2}\;\right)$
That means the approximation was too rough.
Apr
20
comment Showing $\sum_{n=0}^{\infty} \frac {sin(nx)}n $ converges uniformly
what are your bounds on $d$? just non-zero?
Apr
20
answered Evaluate this infinite product: $\prod_{n=3}^{\infty} \left(\;1-\frac{4}{n^2}\;\right)$
Apr
20
answered UpMultiset Combination-choose 3