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I'm having a hard time to go through this exercise, anyone willing to help me before I go crazy? Thank you so much in advance! Graph the function $f(x)...
Asked on 11/02/2021
1 answerLet $v_1,ldots,v_N$ be linear independent unit vectors in $mathbb{R}^N$ and denote their scaled sum by $s_N = frac{1}{N}sum_{k=1}^N v_k.$ I would like to find a small subset...
Asked on 11/02/2021 by g g
2 answerThis question originates from Folland's problem 2.25. In this problem, first given $f(x)=x^{-1/2}$ when $0<x<1$, and $0$ otherwise.Then consider $g(x)=sum_{n}2^{-n}f(x-r_{n})$, where sequence $r_{n}$ is the...
Asked on 11/02/2021
1 answerIf possible, compute the Jordan normal form of $begin{pmatrix}0 & 1 & 0 \ 0 & 0 & 1 \ 0 & a & b end{pmatrix}inmathbb{R}^{3times 3}$ with ...
Asked on 11/02/2021 by user731634
1 answerI have to find $frac{dE[f(X)]}{dX}$ where $f(X) = X1_{X>a}$ where $X sim N(0,1)$ , $1_{X>a}$ is an indicator function taking value 1 if $X>a$ and...
Asked on 11/02/2021 by ForumWhiner
1 answerLet $Q(x)=x^tAx$ for some square symmetric matrix $Ain R^{ntimes n}$, such that $Q(x)geq0$ for each $xin R^n$. Let $S$ be an affine subspace of...
Asked on 11/02/2021
1 answerA real orthogonal square matrix $Q$ of dimension $n$ is defined such that $Q Q^dagger=I$. The associated linear operation $x in mathbf{R}^n rightarrow Qx in mathbf{R}^n$...
Asked on 11/02/2021
0 answerLet $f, g : [−1, 1]rightarrow mathbb{R}$ be odd functions whose derivatives are continuous. Youare given that $|g(x)| < 1$ for all $x in [−1, 1],...
Asked on 11/02/2021
0 answerLet $mathcal{O}$ be a complete local ring with maximal ideal $mathfrak{m}$.Let $R = mathcal{O}[X_1, ldots, X_n]/(f_1, ..., f_n)$ such that $det( partial f_i/ partial X_j...
Asked on 11/02/2021
1 answerFind all $xinmathbb{R}$ such that $$lim_{ntoinfty}|x^n-langle x^nrangle|=0$$ where $langle trangle$ is the integer nearest to $t$ (eg. $langlefrac{1}{3}rangle=0$, $langlefrac{8}{3}rangle=3$, $langle k+frac{1}{2}rangle$ is not...
Asked on 11/02/2021 by tong_nor
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