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I hereby authorize whoever it may concern to post my comments as answers if they wish, whether as community wiki or otherwise if you like imaginary internet points.


Sep
15
comment Logic when using two (if/then) statements
By the way, your proposition also implies that someone who does not have the flu automatically passes the course.
Sep
14
comment being $\mathbf{a}$ and $\mathbf{b}$ two vectors with same length, how do I expand $(\mathbf{a}^T\mathbf{b})^2$?
I prefer to write it as $a^Tbb^Ta$, because expressions of the form $a^TMa$ where $M$ is a symmetric matrix are very common. The derivative is $2bb^Ta = 2(a^Tb)b$, which you can obtain from that form or via $\nabla(a^Tb)^2=2(a^Tb)\nabla(a^Tb)=2(a^Tb)b$.
Sep
14
comment Ellipsoidal Decomposition: Finding ellipsoids whose sum contains a given ellipsoid
Are you sure you want the Minkowski sum? Take any cylinder enclosing $E$, and let $X$ and $Y$ correspond to its cross-section and axis respectively. Then the volumes of $X$ and $Y$ are (arbitrarily close to) zero while their Minkowski sum still contains $E$.
Sep
14
comment When is 2d sparse numerical integration by Voronoi regions better than using triangular mesh elements
One trivial observation: the Voronoi method is continuous in the sample locations, while the Delaunay method can change discontinuously if the samples are perturbed.
Sep
14
comment When is 2d sparse numerical integration by Voronoi regions better than using triangular mesh elements
If you don't get a good answer here, you might consider asking on scicomp.stackexchange.com.
Sep
14
comment Why does $y = x\sin(\frac{180}{x})$ approach $\pi$?
Geometrically, consider the perimeter of a regular polygon with $x$ sides inscribed in the unit circle.
Sep
13
comment How is $\sqrt{3} * \sqrt{2} = \sqrt{6}$ mathematically possible?
"none of them consider the argument of irrational numbers..." I actually checked for that before I posted the link. See the last few paragraphs of the accepted answer by Arturo Magidin, beginning "Then we move on from the positive rationals (fractions) to the positive reals. This is more complicated, as it involves "filling in gaps" between rationals. ..."
Sep
13
comment If multiplication is not repeated addition
The link in the answer is now broken, but here's a currently working one: What Exactly is Multiplication?
Sep
13
comment How is $\sqrt{3} * \sqrt{2} = \sqrt{6}$ mathematically possible?
Previously: If multiplication is not repeated addition, what is it?
Sep
12
comment Find the area where dog can roam
By the way, this is described as the goat problem on MathWorld (don't be misled by the first diagram on the page; it deals with both the interior and the exterior cases).
Sep
11
comment Find the area where dog can roam
Although, given that this question already has more votes and a complete answer, perhaps we should close that older question as a duplicate of this one...
Sep
11
comment Converting non-continuous angle to 360
Depends on where you want the zero and in what direction you want the angles to increase. But the simplest thing would be to just add 180. Then the bottom is 0 and angles increase clockwise.
Sep
11
comment linear solution of curve fitting on multiple linear functions differing by a multiplier
I guess this is essentially coordinate descent on the total squared error. Since the objective is smooth, the procedure should converge, but I don't know how quickly.
Sep
9
comment How can I find the unit vector that minimizes the number of nonzero projections that a set of points has on it?
$\|\mathbf X^T\mathbf w\|_1$ isn't the number of nonzero projections, it's the sum of the absolute values of the projections.
Sep
7
comment Heat Kernel Inverse
If you can take the Fourier transform of $e^{-h(x)^2}$ then it should be pretty simple, no?
Sep
6
comment How to solve $\mathrm {diag}(\mathsf Q^T\mathsf S\mathsf Q)=\mathsf 0$ for $\mathsf S$?
You're right, somehow I was thinking of $\operatorname{tr}(\mathbf1\mathbf1^T)$ instead of $\operatorname{diag}(\mathbf1\mathbf1^T)$ there.
Sep
6
revised How to solve $\mathrm {diag}(\mathsf Q^T\mathsf S\mathsf Q)=\mathsf 0$ for $\mathsf S$?
deleted 2 characters in body
Sep
6
comment Necessary and sufficient condition of $f$ satisfying $f(E[X]) - E[f(X)] > 0$
Hint: Consider a random variable $X$ which can take only two values. Are you familiar with the definition of a convex function?
Sep
6
comment How to calculate peakiness or uniformity in histogram?
Test the goodness of fit of the histogram to a uniform distribution?
Sep
6
comment Is 0.9 repeating = 1 disproved by asymptotes?
$0.000\ldots1$ is not a number that exists. So your friend's argument is based on a function that does not exist. One might as well argue that if you had a function that was a unicorn, the slope of the unicorn would be $0.999\ldots$