15,403 reputation
33683
bio website suvrit.de
location Internet
age
visits member for 5 years
seen 1 hour ago

Researcher in Optimization and Machine Learning.

Hobbyist in Inequalities, Matrix Analysis, Combinatorics, Algebra, etc.

I'm here mostly to learn mathematics!


1d
comment Embedding graphs into hyperbolic spaces
Every CAT(k) space with $k < 0$ is $\delta$-hyperbolic...
2d
comment Errata database?
@ConradoCosta this site might be valuable, but a bit tricky if people end up discussing "work officially under review" and not yet published. In some sense, if Mathscinet would have a "discussion" facility available, that would nail this problem proposed in your area51 proposal...
2d
answered Embedding graphs into hyperbolic spaces
Aug
23
comment Matrix equation $XAXBXC=I$
@RobertBryant Thanks again!
Aug
23
revised Matrix equation $XAXBXC=I$
changed answer based on Robert's feedback!
Aug
23
comment Matrix equation $XAXBXC=I$
@RobertBryant: Thanks for clarifying this! I was worried that I am wrongly invoking Brouwer, and indeed I was. Surprisingly, the Matlab iteration that I wrote, succeeds fairly often; maybe Matlab's sqrtm is picking up a "reasonable" square-root.
Aug
23
comment Why does $d^n \exp(-x-x^{-1})/(dx)^n$ only have $n$ positive real zeroes?
@DavidSpeyer Does the nonlinear recurrence given by Terry Tao fits within the world of cluster algberas? Just curious!
Aug
23
revised Matrix equation $XAXBXC=I$
added a note about brouwer (because previously I used it incorrectly)
Aug
23
revised Matrix equation $XAXBXC=I$
added a note about brouwer
Aug
23
comment Matrix equation $XAXBXC=I$
Ok, I think under suitable assumptions on $B$ and $C$, perhaps this could be made to have a unique "local" solution (in terms of the matrices being within an "injectivity radius")...
Aug
23
revised Matrix equation $XAXBXC=I$
removed logarithmic distance...
Aug
23
revised Matrix equation $XAXBXC=I$
added matlab code
Aug
23
answered Matrix equation $XAXBXC=I$
Aug
23
comment Matrix equation $XAXBXC=I$
In the case where it is ok to compute the square-roots, a numerical computation seems to yield an $X$ that solves the equation mentioned by Terry Tao. In particular, I run the "fixed-point" iteration: $W \gets B\sqrt{W}^*C$ to "convergence" and set $X=\sqrt{W}^*$; this seems to satisfy the equation!
Aug
19
comment Important formulas in Combinatorics
@darijgrinberg: I agree; also, in particular, this is described much better both in the question and in the answers here: mathoverflow.net/questions/73385/…
Aug
18
comment Important formulas in Combinatorics
One of my favorites is the Cauchy identity (a fundamental product-sum relation): $\prod_{i,j}(1-x_iy_j)^{-1} = \sum_\lambda s_\lambda(x)s_\lambda(y)$. Even though this may follow from the MacMahon master theorem, its singular elegance deserves individual mention.
Aug
17
comment Largest eigenvalues distribution of tridiagonal symmetric random matrix
To me a Skew-symmetric matrix has $a_{ij}=-a_{ji}$ which is not the case here. Here it is just a usual symmetric matrix with zero diagonal...
Aug
17
comment Largest eigenvalues distribution of tridiagonal symmetric random matrix
why is it "skew"?
Aug
17
comment Proof for the derivative of the determinant of a matrix
This question really belongs to math.SE and I'm sure even there it's been asked a few times already! Voting to close.
Aug
15
comment Which sets of roots of unity give a polynomial with nonnegative coefficients?
Maybe, the following related result of Kellog is helpful: Let $A$ be a complex $n\times n$ matrix. If all its elementary symmetric functions are positive (so that the characteristic polynomial has alternating signs), then the spectrum of $A$ lies in the set $\{z : |\text{arg}z| \le \pi - \pi/n\}$....