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I was requested to find the congruence of $15^{81}mod{13}$ without using Fermat's theorem (since that is covered in the chapter that follows this exercise). Of course I know that...
Asked on 12/13/2021
2 answerI have two functions $f(x,y)=x^4+y^4 -xy$ and $g(x,y) = x^2$. I know that these two functions "touch" at $(x,y,z) = (0,0,0)$ My question is, how do I...
Asked on 12/13/2021
3 answerLet $T$ be a linear operator.For any underlying normed spaces it holds that$$ker(T)^{bot} subset overline{im(T^*)},$$but if they are both Hilbert spaces we get$$ker(T)^{bot}...
Asked on 12/13/2021 by Rino
1 answerI have been reviewing some integration techniques and have been searching for tough integrals with solutions online. When I was going through the solution, however, I found a discrepancy between...
Asked on 12/13/2021 by Mjoseph
2 answerI have a bunch of points in 3D all on the same plane, having the general equation$$hat{mathbf{n}}cdotleft(mathbf{r}-mathbf{r}_0right)=0$$The unit normal is computed by using 3 points...
Asked on 12/13/2021 by Alexander Cska
1 answerMy question is similar to this question, but I am trying to find a complementary subspace of a subspace that is not in $mathbb R^n$. I am trying...
Asked on 12/13/2021 by Jon G
1 answerI am required to prove that in the ring $R=mathbb{Z}[sqrt{-7}]$ (where $8=2^3=(1+sqrt{-7})(1-sqrt{-7})$)$$sqrt{I}=langle2,1+sqrt{-7}rangle$$where $I=8R$ I am really struggling with this, can someone give me a...
Asked on 12/13/2021
1 answerLet an orthonormal basis of $Bbb{R}^n$ be ${e_1,dots,e_n}$, and $U$ be a subspace in $Bbb{R}^n$. Can we construct the orthonormal basis of $U$ by taking...
Asked on 12/13/2021 by ryuta osawa
1 answerI'm a hobbyist programmer, and not much of a mathematician. I'm trying to model something like the seasonal change in day length. There are two other questions here...
Asked on 12/13/2021 by SaganRitual
3 answerI am reading the paperAlan Edelman, Tomas A. Arias, Steven T. Smith, The geometry of algorithms with orthogonality constraints, SIAM Journal on Matrix Analysis and Applications, Volume...
Asked on 12/10/2021 by gcc
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