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2d
reviewed Approve Prob. 3 (b), Sec. 27 in Munkres' TOPOLOGY, 2nd ed: How does the $K$-topology on $\mathbb{R}$ differ from the usual topology?
2d
reviewed Approve Commutative version of hyper operators.
2d
comment Divisibility of polynomials in a subfield of a field.
@azimut Whenever I am working on a problem I call the relevant property "good" just for brevity ;-). The notion of goodness in this case is completely ad hoc, just for the problem, but who knows? perhaps in some distant future it will become important!!
May
23
answered Divisibility of polynomials in a subfield of a field.
May
19
revised Units in a finite ring
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May
19
reviewed Approve Power series as fractions
May
18
revised Isomorphism Between Gaussian Integers Modulo Some Element and the Ring of Integers Modulo it's Norm.
added 1 character in body
May
6
comment Why can't we eliminate $t$?
He (Lang) can't, but you can...you are Jesus Christ after all.
Apr
21
comment $[U \cap H : G \cap H] \le [U :G]$
@ClémentGuérin An unfortunate choice of notation by the OP ($U$ being the ambient group). Anyway, my suggestion for the set of left cosets of $U$ modulo $G$ is...ta-daa! $(U/G)_L$ ($L$ stands for "left").
Apr
16
reviewed Approve Positive solutions of $893x - 2432y = 19$
Apr
10
comment Let $A,B$ be two $3\times 3$ matrices with complex entries, such that $BA^2=A^2B$. Prove that $\det(AB-BA)=0$
I have one question: why $3\det(AB-BA)=\mathrm{trace}\bigl[(AB-BA)^3\bigr]$?
Apr
10
comment Let $A,B$ be two $3\times 3$ matrices with complex entries, such that $BA^2=A^2B$. Prove that $\det(AB-BA)=0$
My friend, it seems that you are well aware of the property $\mathrm{trace}(WZ)=\mathrm{trace}(ZW)$. Use this property one more time on your last line!!! (take $W=A, Z=BABAB$).
Apr
3
reviewed Approve A question regarding rational functions being onto.
Apr
3
comment Is there a closed-form of $\sum_{n=1}^{\infty} \frac{\sin(n)}{n^4}$
I would try to work with the imaginary part of the series $\sum_{n=1}^\infty\frac{e^{inx}}{n^4}$, and afterwards to evaluate at $x=1$...I am lazy now, sorry.
Mar
28
reviewed Approve Why are two permutations conjugate iff they have the same cycle structure?
Mar
28
reviewed Reject Matrix can be orthogonally diagonalized iff its eigenvectors are linearly independent
Mar
23
awarded  Revival
Mar
22
answered Is the following set connected given that the union and intersection is connected
Mar
19
comment Find a subring $D$ of ring $D'$ such that: $D'$ is a UFD but not a field, and $D$ is an ID but not a UFD.
ID=Integral Domain?
Mar
13
revised When, how & who first gave this calculation of $\pi$
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