Reputation
2,782
Next privilege 3,000 Rep.
Cast close & reopen votes
Badges
7 15
Newest
 Custodian
Impact
~52k people reached

Aug
26
comment Show that there exists holomorphic $f$ such that $f^2=\frac{\sin z}{z}$
I'm assuming that by "radius of convergence of $f$" you mean "radius of convergence of the power series of $f$", right?
Aug
26
comment Solution for ODE $\dot{x}=F(x)$ with $F:\mathbb{R}\rightarrow\mathbb{R}$ smooth, periodic & positive.
Are you assuming that $p$ is a multiple of the period of $F$? Otherwise your last equality in the proof of part 1 does not hold...
Aug
20
comment Assumption in PDE theory
What's the equation that is solved by $u$?
Aug
19
comment Find eigenvalues of operator
Aaaah, but that brings in all the eigenvectors and shuffles together the eigenvalues...
Aug
19
comment Find eigenvalues of operator
Sure, but you can always expand $x_i,x_j$ on the eigenvector basis of $A$, no?
Aug
19
comment Find eigenvalues of operator
Well, I'm puzzled then. Cause if that's the definition of $x_ix_j$, then the statement should be true, since $$ A(x_ix_j)=Ax_i Ax_j = \frac{1}{2}(Ax_i (Ax_j)^T + Ax_j (Ax_i)^T))=\frac{\lambda_i\lambda_j}{2}( x_ix_j^T+x_jx_i^T)=\lambda_i\lambda_j x_ix_j. $$ Edit: assuming $x_i,x_j$ are eigenvectors of $A$.
Aug
19
comment Find eigenvalues of operator
So, is $x_ix_j$ the same as the symmetric part of the matrix $x_i x_j^T$ (or better, the vectorization of that)?
Aug
19
comment Find eigenvalues of operator
Can we assume that $A$ is injective? Also, when we write $x_ix_j$, what do we mean?
Aug
19
answered average of an inequality
Aug
19
comment How to analyze convergence of non-linear difference equation (recurrrence relations)
You probably meant "and if it's greater it's divergent, right?
Aug
19
revised Proof given A,B is invertible, involving transposes
deleted 1 character in body
Aug
19
comment Proof of QR Algoirthm Convergence
Have you tried Matrix Computations, by Golub and Van Loan? I think it's fairly good. Does not get lost in every single detail, but proves most of the results.
Aug
19
comment Integrating $ \int_0^\infty \frac{x^5}{e^x+1} \, dx $
Nice solution. Just one thought: if the integral is in the Lebesgue sense, I think this works, since Dominated Convergence lets you switch integral and series. But if the integral is the improper Riemann integral, then you need uniform convergence, which you have only in $[a,\infty)$, for any $a>0$. Hence, I believe that, formally, one should do the computation for the integral from $a>0$ to $\infty$, and then let $a\to 0$.
Aug
19
comment Find a harmonic function in the first quadrant,
I mean, what kind of solution do you want? A $C^2$ function? An $H^1$ function? What's the set of functions that are candidate to be solutions (provided they are harmonic and satisfy the boundary conditions)?
Aug
19
comment Find a harmonic function in the first quadrant,
Well, in what space are you looking for solutions?
Aug
19
answered Constant rank for an analytic matrix
Aug
19
comment Constant rank for an analytic matrix
Is this matrix guaranteed to be singular for every $z\in\mathbb{C}$? Also, is this $r$ required to be the same for all $z\in\mathbb{C}$?
Aug
18
comment How do I find the minimum resultant of multiple vectors?
Wrt what norm are we looking for a minimum?
Aug
18
reviewed Edit Is this linearly independent? What is the dimension span?
Aug
18
revised Is this linearly independent? What is the dimension span?
TeX edits.