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As the title says, both $A$ and $B$ are $ntimes n$ matrices, I want to prove the Null spaces $Null (A)$ = $Null(BA)$. I do...
Asked on 11/18/2021
1 answerLet $E$ be a vector space over $mathbb{C}$ such that $text{dim}(E)=n in mathbb{N}$. Let $mathcal{B}:={e_1,e_2,cdots, e_n}$ be a basis of $E$. I know that if...
Asked on 11/18/2021
3 answerConstruct a topology $mathfrak{T}$ on $mathbb{Z}$ such that $mathbb{Z}$ is Hausdorff and non-discrete with respect to $mathfrak{T}$. $textbf{My idea}$ : We know that $mathbb{Q}$...
Asked on 11/18/2021 by UDAY PATEL
3 answerQuestion: if $sum y_n$ is "any" rearrangement of series $sum x_n$ , where $sum x_n$ is series of positive terms. Then, if $sum y_n$ diverges...
Asked on 11/18/2021 by Akash Patalwanshi
2 answerI've come across a question which states that one can prove $f:mathbb{R} rightarrow mathbb{R}$ is Lipschitz iff $f$ is absolutely continuous and there exists $M in mathbb{R}$...
Asked on 11/18/2021
2 answerI remember in a numerical analysis class, the prof showed the class, $$lambda_{min}(A) |x|_2^2 leq x^T Ax leq lambda_{max}(A) |x|_2^2$$ where I am assuming that $x in mathbb{R}^n$,...
Asked on 11/18/2021
1 answerSuppose we have a sequence of random variables ${X_n}$ such that $mathbb{E} [|X_n|^2] = a_n + c$ where $a_n to 0$ is a decreasing sequence of positive...
Asked on 11/18/2021 by user3294195
1 answerI encounter a problem for Elliptic integral, to find the exact $C$ for $$int_{0}^{1} {frac{mathrm{d}x}{sqrt{(1-x^2)(1-(kx)^4)}}} sim Cln(1-k)$$ as $kuparrow1;(0<k<1)$. to establish such asymptotic behavior around $kuparrow1$...
Asked on 11/18/2021 by Nanayajitzuki
1 answerHow to prove that$$lim_{nmapsto 0}[(psi(n)+gamma)psi^{(1)}(n)-frac12psi^{(2)}(n)]=2zeta(3) ?$$I encountered this limit while I was trying to solve $int_0^1frac{ln xln(1-x)}{x(1-x)}dx$ using the derivative of beta function but I have no...
Asked on 11/18/2021
2 answerSo I am not really sure what to do. I know by the definition of divisibility there must exist some integers $k$ and $l$ such that $$...
Asked on 11/18/2021 by MathyViking
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