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Sep
1
comment Question regarding Eigen Value Decomposition and Singular Value Decomposition
The above suggests that $A=U_1 D V^*$, so $A^*A = V D^2 V^*$ (that is, look at $V$ not $U$, $U_1$). Also, the eigenvalues of $A^*A$ may not be ordered in the same way as the singular values.
Aug
31
revised How to calculate distance from the International Space Station given coordinates?
added 22 characters in body
Aug
31
comment How to calculate distance from the International Space Station given coordinates?
I'm not sure what you are having issues with. Just substitute the various values in and compute. The radius of the Earth is about 6,400km, the ISS is about 400km above the surface, so $r_1 =6400, r_2 = 6800$. Then substitute the longitudes & latitudes (in radians) to compute the $(x,y,z)$ coordinates of the two points and then compute the Euclidean distance between the two points.
Aug
31
comment How to calculate distance from the International Space Station given coordinates?
$p$ is a function $p:[0,\infty) \times [0,2 \pi] \times [-\pi,\pi] \to \mathbb{R}^3$. The $k$ is $1$ or $2$ and just selects one of a pair of coordinates.
Aug
31
revised A question on numerical range
sp.
Aug
31
answered How to calculate distance from the International Space Station given coordinates?
Aug
31
comment Existence of primitive of a continuous function on an interval (a,b)
@TonyPiccolo: No; as long as $f$ is continuous it is bounded on any compact subinterval, so $F$ is well defined. For example, take $f(x) = {1 \over x}$ on $(0,2)$, then $F(x) = \log x$.
Aug
30
comment If $\bar X$ is open, then $X=\bar X$.
What do you mean by $\overline{X}$?
Aug
30
answered Existence of primitive of a continuous function on an interval (a,b)
Aug
29
comment Physical interpretation for the curl of a field
It is a measure of the rotation of vector field $F$. Think (loosely) of a tiny sphere 'floating' in the vector field, whose surface moves at the same speed as the field. The sphere will have some motion and rotation. The curl measures this rotation.
Aug
29
comment Riemann's Hypothesis Proof
Rough crowd. Keep trying.
Aug
29
comment If $(a+b)^n=\sum_{k=0}^{n}{n\choose k}a^{n-k}b^kc_k$, then $c_k=1$?
@MarkusScheuer: Thanks for the clarification, it is no problem at all. The downvote as such doesn't matter, the reason does. I obviously overreacted above.
Aug
29
comment Eigen vectors of a matrix multiplied with its transpose
Not necessarily, take $A$ it be orthogonal, for example.
Aug
29
comment All continuous functions are analytic
How do you define the anti derivative?
Aug
29
comment If $(a+b)^n=\sum_{k=0}^{n}{n\choose k}a^{n-k}b^kc_k$, then $c_k=1$?
Why the downvote again? It answers the question (whether $n$ is fixed or not) and is correct. This sort of pettiness really keeps me away from MSE.
Aug
29
comment Law of Large Numbers - utility/difficulty of various versions.
Nice question & preamble; I don't get the downvotes.
Aug
28
comment If $(a+b)^n=\sum_{k=0}^{n}{n\choose k}a^{n-k}b^kc_k$, then $c_k=1$?
I am just curious, given your accepted answer: You answered yes to my question above, which would mean that the indicated answer is incorrect. Can you clarify what you meant in your question so that others don't waste time answering the wrong question.
Aug
28
comment If $(a+b)^n=\sum_{k=0}^{n}{n\choose k}a^{n-k}b^kc_k$, then $c_k=1$?
Why the downvote?
Aug
28
comment If $(a+b)^n=\sum_{k=0}^{n}{n\choose k}a^{n-k}b^kc_k$, then $c_k=1$?
The OP indicated that the equality holds for all $n$. (What does the $\gcd$ have to with anything?)
Aug
28
revised If $(a+b)^n=\sum_{k=0}^{n}{n\choose k}a^{n-k}b^kc_k$, then $c_k=1$?
added 369 characters in body