Eric Haengel
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 Feb22 awarded Nice Question Oct22 awarded Notable Question Oct4 awarded Popular Question Aug12 awarded Yearling Jul16 awarded Good Answer Jul2 awarded Curious Jun11 awarded Popular Question Apr28 awarded Popular Question Apr20 awarded Popular Question Apr1 awarded Popular Question Feb6 awarded Popular Question Aug12 awarded Yearling Apr2 awarded Popular Question Feb28 comment How to calculate inverse of a matrix Where did you find this matrix? There may not be a useful closed-form solution, in particular because when $m$ is a large number that matrix becomes fairly ill-conditioned to start with. I don't mean to imply that there is no closed form solution, but that formula is likely not going to be numerically stable. It may be better to try to invert that matrix numerically with preconditioned LU decomposition, or some other algorithm which can invert ill-conditioned matrices. Feb28 comment Finding a primitive element for a field extension It seems to me like $\mathbb{Q}(2^{1/3}, 2^{1/4}) = \mathbb{Q}(2^{1/12})$, so $2^{1/12}$ is your primitive element. Feb22 comment Find a majorizing function Oh, were you trying to use the dominated convergence theorem to switch the limit and integral? Is finding the value of that limit the original problem you started with? Feb21 comment Harmonic Functions and Harmonic Conjugates on an Annular Domain Ok, sorry it just looked a lot like it haha. Feb21 comment Find a majorizing function It seems to me that as long as $n \geq 1$ the function on the left is unbounded, so there is no solution unless you assume $n \in (0, 1)$, and even then the function is not integrable because $|1/(n + n^2 \sin(xn^{-2})) |$ is periodic and integrates to a finite number on each period. Hence its integral over $(0, \infty)$ is infinite. Feb21 comment Integral of $1/z$ over the unit circle The arguments between two complex numbers above and below the real axis will differ by $2 \pi$, but $\log(z) = \log(|z|) + i \arg(z)$. There is a factor of $i$ in front of the $\arg(z)$ term, so that's where the $i$ comes from. Feb21 answered Integral of $1/z$ over the unit circle