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1h
comment How to find the discrete probability vector given a transition probability matrix?
The invariant probability vector is a probability vector, and it is an eigenvector for the eigenvalue 1. So all you have to do is find a vector in the (left) nullspace of $A-I$.
1h
answered Asymptotic result about analytic number theory
2d
comment help in approaching this problem
This wouldn't be a problem from an ongoing contest, would it?
2d
comment Coin transport chain game
Shooting up a movie theater also receives attention. More justification is needed.
2d
comment Doubt regarding trigonometric equation
If you take the square root on both sides of $(-7)^2=7^2$, do you get $-7=7$?
2d
comment When do eigenvectors converge?
$A_n$ has $N$ eigenvalues. Which one is $\lambda_n$?
Apr
17
comment Coin transport chain game
I suppose it goes without saying that you will have to read up on Nim to take full advantage of Ross' answer & comment. But Ross has given you a link, so you should be OK on that. Once you've done that, you can post a complete answer, if you like.
Apr
17
comment Coin transport chain game
So, why didn't you just edit it?
Apr
16
comment How to prove that it is a group?
Well, don't you want to work that out for yourself, now that you've seen how to do i?
Apr
16
comment Coin transport chain game
Why did you post this as math.stackexchange.com/questions/755036/… and then delete it and then post it again?
Apr
16
comment vertex magic total labelings
A definition of "vertex-magic total labeling" would also be appreciated.
Apr
16
comment A question on the expansion of $(1-x)^n$
See en.wikipedia.org/wiki/Bernoulli's_inequality
Apr
16
answered How to prove that it is a group?
Apr
16
comment Largest determinant of a real $3\times 3$-matrix
I'm pretty sure that in the real case, and even for $n\times n$ matrices, the maximum is achieved when the entries are taken from the set $\{-1,1\}$, but I don't know a good reference offhand. Maybe a treatment of Hadamard matrices would cover this question. The opening paragraph of en.wikipedia.org/wiki/Hadamard_matrix backs me up.
Apr
16
comment Construct matrix of ones and zeros based on sequences
Another source is Ryser's book, Combinatorial Mathematics. It's in the MAA Carus Monograph series.
Apr
16
comment Value of $i^2$ in complex numbers
How are you defining $i$, akanksha? If, like the rest of us, you are defining it by $i^2=-1$, then of course $i^2=-1$.
Apr
16
comment Counterexamples in set theory
Also math.stackexchange.com/questions/749053/… and math.stackexchange.com/questions/744502/…
Apr
16
revised Finding Mod Value
edited tags
Apr
16
comment Eigenvalue of linear operator
Compute $T(f)$ for each $f$ in your standard basis. The results will give you the matrix for $T$ (with respect to that standard basis).
Apr
16
comment Changing research area in grad school
I second the idea of talking this over with your supervisor, or at any rate with someone at your institution. They know you a lot better than we do.