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Sophomore Graduate Student in Mathematics


Nov
15
comment $I_m - AB$ is invertible if and only if $I_n - BA$ is invertible.
This is how I did the problem the first time, but then I forgot how I did it and was stuck. :P Thanks :-)
Nov
15
comment $I_m - AB$ is invertible if and only if $I_n - BA$ is invertible.
Thank you for another nice answer.
Nov
15
comment $I_m - AB$ is invertible if and only if $I_n - BA$ is invertible.
Thank You. It makes the proof quite obvious now. :D
Nov
14
comment Is this $SL_3(\mathbb{F_2})$ look like?
@sos440 +1 for the complete list
Nov
3
comment How many decimal places are needed for incremental average calculation?
@JernejJerin If you are satisfied with the answers, you might consider accepting them, else you might want to indicate what more information you want.
Oct
29
comment Good problem book on Abstract Algebra
I unaccepted your answer and instead accepted Dedalus's answer since on retrospective, I have found some of the book Exercise in Algebra and other books a more concentrated source of problems. I hope you don't mind.
Oct
26
comment Determinant of a Modified Jacobian of a Function
That's all there to it?! I came up with a similar but infinitely cruder solution, however, I was not sure of this. Also, I was thinking there might be some rank-related solution also. Anyway, thanks. :-)
Oct
18
comment How to solve this equation:$\sqrt{x-\sqrt{x-\sqrt{x-\sqrt{x-5}}}}=5$
@vesszabo No, he uses it in this direction, but goes upto infinity, however, I am not sure of the formal justification of the step.
Oct
18
comment How to solve this equation:$\sqrt{x-\sqrt{x-\sqrt{x-\sqrt{x-5}}}}=5$
The logic is similar to $\sqrt{x-5} =5 \implies \sqrt{x-\sqrt{x-5}} = 5$
Oct
4
comment Dual basis of a shrinking unconditional basis
@TrzyTrypy You can delete the question yourself and that would be the best method to do so.
Sep
28
comment Cycling Digits puzzle
Added some more explanation. I hope it is more clear now.
Sep
28
comment Cycling Digits puzzle
@PerManne Yup. Sorry about that, I was going to update it.
Sep
26
comment field generated by a set
Where I mean $K$ by $G_{S}$
Sep
26
comment field generated by a set
@JasonDeVito I guess your objection is invalid, since we are talking about $S$ generating $R$, rather than $S$ being $R$ itself. Since, if $\frac{1}{10} \in S$ then $\frac{k}{10} \in G_{S}$ where $k \in Z$.
Sep
26
comment field generated by a set
@FortuonPaendrag You say that your proof is flawed. I think it would be good if you can probably indicate why do you think it is flawed in the answer itself.
Sep
25
comment In what spaces does the Bolzano-Weierstrass theorem hold?
@KevinCarlson Its okay. I do not mind.
Sep
25
comment In what spaces does the Bolzano-Weierstrass theorem hold?
I guess not. So, basically, we want to find conditions for total boundedness and completeness from the metric of the space and the set of points? Is this true?
Sep
25
comment In what spaces does the Bolzano-Weierstrass theorem hold?
@KevinCarlson Okay. If I say that total boundedness of a closed subspace of a complete metric space implies compactness and vice-versa. Will that address the question enough?
Sep
22
comment How to Find a Finite-Difference Matrix
You might want to learn more about the finite difference methods. I am sure there are enough textbooks on the same that explain the process in detail.
Sep
22
comment Non surjectivity of the exponential map to GL(2,R)
Try $A = \left(\matrix{1 & 0 \\ 0 & -2}\right)$. And show that this cannot be an exponential, since exponential cannot be negative in $\mathbb{R}$.