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Feb
28
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.
Feb
28
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.
Feb
22
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?
Feb
21
comment Harmonic Functions and Harmonic Conjugates on an Annular Domain
Ok, sorry it just looked a lot like it haha.
Feb
21
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.
Feb
21
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.
Feb
21
answered Integral of $1/z$ over the unit circle
Feb
21
comment Harmonic Functions and Harmonic Conjugates on an Annular Domain
Is this the purdue math club?