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I was reading Schutz's book on General Relativity. In it, he says that a(n) $M choose N$ tensor is a linear function of $M$ one-forms and $N$...
Asked on 12/01/2021
1 answerHow does one take the derivative for the function $g(x) = int_a^xf(x,t) dt$? $$ frac{d}{dx}g(x) = frac{d}{dx}int_a^xf(x,t) dt $$ For example, how would one find $frac{d}{dx}int_0^x x...
Asked on 12/01/2021 by klein4
1 answerSuppose that $mu$ is a Radon measure on $mathbb{R}$, and let $I(mu)$ be the Stieltjes transform of $mu$, i.e. $I(mu)(lambda)=int_{mathbb{R}}frac{1}{x-lambda},mathrm{d}mu(x)$ for $lambda$ non-real. If...
Asked on 12/01/2021
1 answerThere are obviously real-valued functions $f$ which are bandlimited. Take, for instance, $f = mathrm{sinc}$. Can $f$ be also non-negative at the same time?...
Asked on 12/01/2021 by Muzi
1 answer$( A cap C ) times ( B cap D ) = emptyset$$B cap D = emptyset$$A cap C = emptyset$$A cap D = emptyset$I feel...
Asked on 11/29/2021 by Anonymous Molecule
3 answerSuppose that $Ain M_{n+m}(mathbf C)$ (i.e. a $(n+m)times (n+m)$ complex matrix) is non-singular. Is it always possible to find a permutation matrix $P$ so that ...
Asked on 11/29/2021 by syeh_106
1 answerI'm confused with the expression ${f(x) = ln(e^{x^2})}$.I know the rule ${log_a(x^p) = plog_a(x)}$. So does the given expression reduce to ${x^2ln(e)}$ or ${2xln(e)}$?...
Asked on 11/29/2021 by EVO
3 answerI have this proof: "Suppose by contradiction that $(0, 1)$ is countable. This means we can find asequence $(x_n)$ such that for every $x ∈ (0,...
Asked on 11/29/2021 by Henry Brown
2 answerI know the definition of a bijective linear map $L: V rightarrow W$ (one that is both injective and surjective). However, my book states that it is equivalent to...
Asked on 11/29/2021
1 answerI found this question in a previous year post graduate entrance exam for mathematics.The question was What is the range ofbegin{equation*}frac{200 choose 100}{4^{100}}end{equation*} The choices...
Asked on 11/29/2021 by vib_29
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