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4h
revised Mathematically, why was the Enigma machine so hard to crack?
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5h
revised Explicit linear combination of some matrices
title that suggest how insignificant this question is
5h
revised Verbal question problem help
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6h
revised Equating eigenvalues of Hermitian matrix and correlating symmetric/antisymmetric matricies
added 77 characters in body
6h
comment Equating eigenvalues of Hermitian matrix and correlating symmetric/antisymmetric matricies
Please use $ to delimit formulas rather than `.
8h
revised Prove that the output of the function equals the determinant
deleted 1 character in body
9h
comment One of these two operators is not invertible
Offhand this looks like like one of those cases where the hypothesis $\dim H>0$ is missing.
9h
answered Writing equations without latex (for labelling, classification, structure analysis and rendering according to mathematical meaning)
12h
revised Find the area of this irregular octagon inscribed in a circle
edited title
12h
comment Prove that the output of the function equals the determinant
I think you should write $\delta$ instead of $det$ to avoid suggesting you already know it is the determinant. And you should write it on both sides of the first equation. Also I don't really see the point of introducing a matrix product (which suggest something more profound than what is actually going on), given that you are going to specialise to $\binom{r_1}{r_2}=I_2$ anyway: you could do the latter right away (defining $r_1,r_2$ to be two specific rows), and so avoid the initial matrix product; your derivation remains valid.
12h
answered Prove that the output of the function equals the determinant
22h
comment Cube root of $\omega$
Not clear what you are asking. Apart from $1$ there are two cube roots of$~1$, each with $3$ cube roots; the resulting set is known as that of the primitive $9$-th roots of unity. They are $\exp(2\pi\mathrm i\frac k9)$ for $k=1,2,4,5,7,8$, which you can express in trigonometric terms using Euler's formula.
1d
comment Error in my proof?
No, at best it denotes the square root of that limit.
1d
comment Error in my proof?
(Apart from the fact that infinite expressions are IMO delirious in general unless of a special kind for which meaning is given to them in special way, this one is particularly insidious:) Since there is both an innermost and an outermost square root sign (both visible), there is a serious question about what the dots mean if they suggest infinite repetition (and if it is finite we clearly need to know how many). Are they indexed, from the inside outwards by $\omega+1$ (so after taking the limit take one more root), or some other cardinal, or maybe they are not well-ordered in the first place?
1d
answered Why the radius of convergence and not “areas of convergence” for power series?
1d
comment How to find the degree of an extension field?
Actually, if $r$ is a root of an irreducible rational polynomial of degree $n$, then the degree $[\Bbb Q(r):\Bbb Q]$ is guaranteed to be equal to$~n$. Simply because $r^0=1,r,\ldots,r^{n-1}$ are linearly independent over$~\Bbb Q$ from the hypothesis ($r$ cannot be root of another monic irreducible polynomial as well, since that would make the$~\gcd$ of those distinct irreducibles distinct from$~1$, which is absurd).
1d
answered Under what conditions is a linear automorphism an isometry of some inner product?
1d
comment What's wrong in this equation? (Regarding Euler's eqn)
More precisely for $(a^b)^c=a^{bc}$ to be valid, $a$ has to be a positive real (for exponentiation with non-integer exponent to be well defined in the firs place) and $b$ has to be real. It is allowed that $c$ be any complex number. However it is not sufficient that instead of $b$ being real just $a^b$ is real (even though in that case both sides of the equation are well defined), as your example shows.
1d
answered Does matrix has a underlying basis?
2d
comment Unique factorization consequence
you could just say that the inclusion $bR/(bp)\subseteq E_p$ is trivial. Then when you say the "opposite inclusion", I guess there is not much confusion what that is.