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I'm reading Advanced calculus of several variables by Edwards, C.Henry. On page 6, the author is proceeding with the proof that any $n+1$ vectors in $Bbb{R^n}$ are linearly...
Asked on 11/01/2021
1 answerLet $n$ a positive integer, define $A=left(e^{frac{2i(k-1)(l-1)pi}{n}}right)_{1 leq k,l leq n} $ , evaluate $det(A)$....
Asked on 11/01/2021
1 answerI'm looking for a definition of random $k$-dimensional vector subspace of the Euclidean space $mathbb{R}^d, k, d$ are fixed. I'm guessing one should start with a random basis,...
Asked on 11/01/2021
2 answerThe non-elementary functions $$ F(x) = int sin(x^2)mathrm dx $$$$ G(x) = int cos(x^2)mathrm dx $$ will yield $$ F(x) =sum_{k=1}^{infty} (-1)^k frac{x^{(4k+3)}}{(2k+1)!(4k+3)}$$$$ G(x)...
Asked on 11/01/2021 by Rickard Martensson
0 answerSolve the differential equation $$(D^3-3D^2+4D-2)y = (e^x +cos x),,$$ where $D = dfrac{mathrm{d}}{mathrm{d}x}$.Here, for $e^x$, we place coefficient of $x$ in place of $D$ which...
Asked on 11/01/2021 by piyush mahajan
2 answer$$x_k := sin left(frac{pi k}{3} right),qquad x_{infty} := lim_{k to infty}{x_k}$$I tried to prove by contradiction. Assume limit exists and is $L$. Fix $epsilon=frac{sqrt{3}}{4}$. There exists...
Asked on 11/01/2021 by ovunc
1 answerHere is just a sample problem. Suppose that $V$ is finite dimensional and $S, T in mathcal{L}(V)$. Prove that $ST = I$ if and only if ...
Asked on 03/16/2021 by popping900
3 answerIf a convex function exists $f:mathbb Rto mathbb R$ and satisfies $f(10) = -4$ and $f(20) = 30$, how should I find the smallest value for ...
Asked on 03/15/2021 by jixubi
2 answerI am currently trying to discretize a non-linear problem in order to express it as a MIP.I don't think I am talking exactly of a SOS as order doesn't...
Asked on 03/13/2021 by Kamer73
1 answerIn the figure below of points in $3$-$D$ space, suppose the lengths of the blue segments are all known. Is it possible to determine the lengths of the...
Asked on 03/10/2021 by Apoapsis
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