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 Apr10 comment How many distinct elements are there in $C=\{zw\mid z∈A$,$w∈B\}, z^{24}=1$ and $w^{54}=1$. But this is anyway an algebra problem. Apr6 comment Why are additional constraint and penalty term equivalent in ridge regression? Can you briefly summarize the paper (since the journal version has some pages)? Apr6 comment Why are additional constraint and penalty term equivalent in ridge regression? If $\alpha=0$, does it mean the corresponding $c$ can be any non-negative number, according to the second KKT condition? Jan27 comment Does Euclidean division not work for general polynomials? ED implies PID. But only polynomials of one variable can form a PID. So no. Nov16 comment How to find $x$ such that $\tan5x=\tan x$ and $\sin5x=\sin x$? You are welcome :) Aug12 comment What is the oldest open problem in geometry? I would like to see an animation for a periodic orbit in an obtuse triangle. Jul11 comment Limit of the integral: $\int_0^{\pi/2}\beta^\alpha\exp\left(-\beta\cos(\theta)\right)d\theta$ Shouldn't it be $\lim_{\beta\to+\infty}J_0(\beta)=0$? Illustration. Jul4 comment 'Obvious' theorems that are actually false You may be interested in these books: Counterexamples in Analysis, Counterexamples in Topology, and Counterexamples in Probability. Jul2 comment How to prove that: $\tan(3\pi/11) + 4\sin(2\pi/11) = \sqrt{11}$ How did you reach the $\sum_i \omega^{2i}=0$? Jun19 comment How to evaluate the following integral? $\int \ln(e^x + c)~\mathrm dx$ When faced with $\int f(e^x)\,\mathrm{d}x$, try transform it into $\int u^{-1}f(u)\,\mathrm{d}u$. Jun19 comment Clarification on optimization problem I think for any $\alpha_k$, the objective function is linear. Given that the constraint is also linear, the optimum lies in some corner point. Since $\alpha_5=1$ violates the constraint, so $\alpha_5=0$. Apr20 comment Givens rotation and retraction mapping Thanks. I am fine with the QR/polar decomposition and exponential mapping, but I am not clear about the part of Givens rotation in the text. Also, any references for the "closest" property of polar decomposition? Feb18 comment Homework problem on continuity I think differentiability implies continuity. Jan23 comment $QQ$-plot - Why do we choose the empirical distribution $F_n(x) = \frac {\#\{y \in S \mid y \le x\}} n$, $S$ is sample, for comparison with normal? Just to mention that there is another SE site for statistics: stats.stackexchange.com Jan23 comment Correspondence between an order of rational function field and a Dedekind cut Thanks. Then where does the $a$ come from? It seems to me that $X>_{\mathbb{R}(x)}x\iff X-x>_{\mathbb{R}(x)}0\iff -x >_\mathbb{R}0 \iff x<_\mathbb{R} 0$. Jan8 comment How prove this inequality $(a^2+bc^4)(b^2+ca^4)(c^2+ab^4) \leq 64$ Maybe different patterns of lines, if that's convenient for you. Jan8 comment Set of critical points of polynomial: why finite When you say a polynomial defined on $\mathbb{R}^n$, does it mean a multivariate polynomial with $n$ variables? Jan8 comment How prove this inequality $(a^2+bc^4)(b^2+ca^4)(c^2+ab^4) \leq 64$ Can you use other colors? Since many people have protanopia or protanomaly (like me). Jan4 comment Kullback–Leibler divergence with elements that are $0$ How about additive smoothing? Dec16 comment Find derivative of $f(x)=(x+2)^{(x-1)}$ OK, I get it. It has nothing to do with the logarithm.