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Apr
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Mar
27
comment Eigenvalues are continuous?
@Adam Yes, the functions $x_i(t)$ are continuous. It was stated so in the source I linked to in my previous comment, but I forgot to include it in the answer. I've updated the answer now. Thanks for pointing that out.
Mar
27
revised Eigenvalues are continuous?
added 32 characters in body
Mar
27
comment Prove the number of Hamiltonian cycles of $K_n,_n$ for $n\ge2$ is $\frac{n!(n-1)!}{2}$
@MikeDaas Fair enough.
Mar
27
revised Prove the number of Hamiltonian cycles of $K_n,_n$ for $n\ge2$ is $\frac{n!(n-1)!}{2}$
deleted 6 characters in body
Mar
26
comment Prove the number of Hamiltonian cycles of $K_n,_n$ for $n\ge2$ is $\frac{n!(n-1)!}{2}$
@MikeDaas Sorry, you're correct. I labelled the latter cycle incorrectly the first time. Hopefully it's clear this time.
Mar
26
revised Prove the number of Hamiltonian cycles of $K_n,_n$ for $n\ge2$ is $\frac{n!(n-1)!}{2}$
edited body
Mar
26
answered Prove the number of Hamiltonian cycles of $K_n,_n$ for $n\ge2$ is $\frac{n!(n-1)!}{2}$
Mar
14
comment A doubt in the proof of the Generalized Mean Value Theorem.
You're missing a $g'(c)$ I think.
Mar
13
comment Recurrence relations and limits, tough.
I never said anything about establishing the value of the limit. My point is that $p_n/z^n$ and $\phi_n/z^n$ do not have the same asymptotic behavior, in the sense that $\lim_{n\rightarrow \infty} p_n/\phi_n \neq 1$. So I'm not exactly sure what you mean when you say the two have the same asymptotic behavior.
Mar
13
comment Recurrence relations and limits, tough.
I'm not all too convinced by your last paragraph. The particular solution to the inhomogeneous equation will not be $O(1)$. It will also be $\Theta(z^n)$. Its magnitude is enough to change the limit, as you've noted in the last sentence. So it's certainly plausible that the limit exists, but I don't believe you've proved that.
Mar
11
answered What does the comma mean between two matrices represent?
Mar
9
answered Is the following derivation of how to find $v$ given $a=v'$ wrong?
Mar
9
comment (Green/blue)-eye logic puzzle. Statement validation
Your statements for (1), (2) and (3) are rather imprecise and I'm not too sure what to make of them. What exactly do you mean by "For each one of you, there is a . . . . pair of blue eyes"? Do you mean to say that "the number of pairs of blue eyes" is equal to the number of people? The condition of "being neighbors with" is also a rather imprecise condition. What do you take to be "a neighbor"?
Mar
9
answered A matrix polynomial problem
Mar
7
comment Curl of an integral of a vector field?
I am assuming that you're doing electromagnetism, in which case your integral is an $\mathbf{E}$ sourced by a density $\rho$. In any case, you'll want to apply Faraday's law to find the curl of an electric field.
Mar
6
comment Recurrence relations and limits, tough.
The limit that you establish is weaker than the required result. In particular, it is not true that $p_n/z^n$ tends to $1$. The limit will very much depend on initial conditions.
Mar
5
comment Exterior power of a space of maps $(\mathbb{K}^T)$
The dimensions don't match up. Let's take $|T|=n$. Then $\mathbb{K}^T$ is $n$ dimensional while $\mathbb{K}^{T^p}$ is $n^p$ dimensional. The exterior power is $\binom{n}{p}$ dimensional.
Mar
5
comment geometrical and algebraic interpretation of $i$
I'm not sure what your answer means either, and the person probably had a specific example in mind. Historically, $i$ was invented as a formal object to solve cubic equations. People found that they could not extract the roots of cubics (even the real ones) without encountering the object $\sqrt{-1}$. Of course they didn't have any formalism for really dealing with this object back then, but it was a necessary crutch. The whole modern view of $\mathbb{C}$ as a field extension came much later.
Mar
3
comment Finding the inverse of a matrix given an equation
Can you find the inverse of the matrix on the right-hand side?