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12h
answered How to show that $f$ is a straight line?
12h
revised Drawing critical points together with a level curve
added 2 characters in body; edited tags
12h
answered Drawing critical points together with a level curve
13h
comment Drawing critical points together with a level curve
You can use wolfram alpha for help: wolframalpha.com/input/?i=plot+f(x,y)+%3D+(sin+x+%2B+sin+y)%5E2, wolframalpha.com/input/…
14h
answered Identifying a function
14h
comment Basis for 4th degree polynomials such that integral of $p(x)$ from $-1$ to $1$ equals $0$
If you have meant for $\mathcal{P}_4(\mathbb{R})$ to contain polynomials of degree less than or equal to four, then add another coefficient $a_4$ to $p(x)$ and repeat the calculation. Your basis for $U$ will then consist of four vectors.
14h
revised Basis for 4th degree polynomials such that integral of $p(x)$ from $-1$ to $1$ equals $0$
added 3 characters in body; edited title
14h
answered Basis for 4th degree polynomials such that integral of $p(x)$ from $-1$ to $1$ equals $0$
14h
reviewed Close Is the sequence $s_n= \frac{\sin\frac\pi2}{1\cdot 2}+\frac{\sin\frac\pi{2^2}}{2\cdot 3} + \dots + \frac{\sin\frac\pi{2^n}}{n\cdot(n+1)}$ convergent?
14h
reviewed Close Probability of last $3$ captains photo (stars and bars)
14h
reviewed Leave Open Regression concepts clarified.
14h
reviewed Reopen Monomial Algebras problem : lcm
14h
reviewed Close What is the probability of observing three or fewer 6s when rolling a fair die twenty times?
14h
revised Proving that $u$ and $v$ are linearly independent, given the independence of $T(u)$ and $T(v)$
edited title
14h
answered Proving that $u$ and $v$ are linearly independent, given the independence of $T(u)$ and $T(v)$
14h
revised Proving that $u$ and $v$ are linearly independent, given the independence of $T(u)$ and $T(v)$
added 6 characters in body; edited title
14h
revised Finding all eigenvectors and eigenvalues of a linear operation on a function
added 50 characters in body
14h
answered Finding all eigenvectors and eigenvalues of a linear operation on a function
15h
comment How do I find a smooth map from complex Gr(k, n) to real Gr(2k, 2n)?
@user311698 It still doesn't make much sense as the dimension of the range is larger than the dimension of the domain. You can have a smooth injective map, described by Malkoun and myself.
16h
comment Explanation of “weight function” of inner product in Hilbert space
Now, $\theta$ and $\varphi$ are the spherical coordinates and the appropriate inner product here takes in the account the geometry of the sphere - it should be modified by a "weight" function (which is the volume form of the sphere). That is, $\left< f, g \right> = \int_{0}^{2\pi} \int_0^{\pi} f(\theta, \varphi) \overline{g(\theta,\varphi)} \sin (\theta) \, d \theta d \phi$. This is not a weight function per se (as $\sin(\theta)$ is not positive) but you get the idea. With this specific choice of the inner product, the spherical Laplacian becomes self-adjoint.