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Nov
14
awarded  Popular Question
Oct
30
comment How to find $\int_0^1f(x)dx$ if $f(f(x))=1-x$?
@G-man yes. agree
Oct
30
awarded  Enlightened
Oct
30
answered $\epsilon - \delta$ definition of a limit?
Oct
30
awarded  Nice Answer
Oct
30
awarded  Yearling
Oct
30
answered How to find $\int_0^1f(x)dx$ if $f(f(x))=1-x$?
Jun
22
comment Decomposing Toeplitz matrix
can you try iterative method? I knew there is a book on this topic (but I never read it) epubs.siam.org/doi/book/10.1137/1.9780898718850
Feb
10
answered Markov Chain with heterogeneous transitions
Jan
24
comment Building a proper homomorphism between groups.
I think you can just simply write $f(x) = f(g^m) = m$
Dec
16
awarded  Caucus
Dec
9
asked Continued fraction approximation to a function and its derivative
Jul
2
awarded  Curious
May
25
awarded  Enthusiast
Apr
15
comment Reliability of linear regression to predict future
I think popovitsj may want to discuss the concept of consistent estimator and also Gauss-Markov theorem?
Apr
8
comment How to show this: $\sum_{k=2}^{n}\frac{\ln{k}}{k^2}\approx \ln{n}\cdot\left(\zeta_{n}{(2)}-\frac{\pi^2}{6}\right)+C$
To relate $\zeta'(x)$ and $\zeta(x)$ and something like $f(b)-f(a)=f'(c)(b-a)$ for some $c \in (a,b)$. Imagine $\ln(n)$ is $f'(c)$, $\zeta_n(2) - \zeta(2)$ is $b-a$.
Apr
8
comment How to show this: $\sum_{k=2}^{n}\frac{\ln{k}}{k^2}\approx \ln{n}\cdot\left(\zeta_{n}{(2)}-\frac{\pi^2}{6}\right)+C$
I don't have an answer. Did you try any method related to mean value theorem? The resulting formula looks like it
Apr
3
comment Powers of permutation matrices.
sorry I misread your question
Apr
3
comment Powers of permutation matrices.
because all possible permutation is finite, prove it by contradiction.
Mar
26
comment Why are we interested in irreducible representation but not faithful representation?
Thank you very much for your answer. I have spent many times on finding out in particle physics (self-study and google around, I am not in an university) to try to figure out your example. Basically, the symmetry of nature (in standard model) is $SU(3) \times SU(2) \times U(1)$ somehow describe the nuclear strong force, weak force and electromagnetic force. Then, the irreps of an element of $SU(3) \times SU(2) \times U(1)$ would describe a particle. Why trivial representation is important is that it is used to describe an elementary particle. Did I get it right?