bio | website | suvrit.de |
---|---|---|
location | Internet | |
age | ||
visits | member for | 4 years, 4 months |
seen | Nov 24 at 11:16 | |
stats | profile views | 8,604 |
Researcher in Optimization, Machine Learning, etc.
Hobbyist in a small fraction of the world of Inequalities, Matrix Analysis, Noncommutative polynomials.
I'm here mostly to learn old and new mathematics!
Nov 29 |
awarded | Enlightened |
Nov 29 |
awarded | Nice Answer |
Nov 19 |
reviewed | Close Noncommutative version of Littlewood's First Principle |
Nov 18 |
comment |
Is the product of sine principal angles a semi-metric on Grassmannian?
Say $U'U=I_d$ and $V'V=I_d$, then unless I'm completely overseeing something obvious, it is pretty easy to find counterexamples to the triangle inequality. |
Nov 17 |
reviewed | Leave Open Can an algorithm decide whether a program computes all strings? |
Nov 15 |
reviewed | Leave Open How to prove that a kernel is positive definite? |
Nov 14 |
answered | How to prove that a kernel is positive definite? |
Nov 12 |
comment |
Combinatorial Interpretation of Generalized Stirling numbers
did you try at least googling? |
Nov 6 |
awarded | Nice Answer |
Nov 6 |
revised |
Eigenvectors of a particular transition matrix
added proof of eigenvalues; removed intuition behind the discovery of the solution. |
Nov 3 |
comment |
Proving that the kernel of this matrix is of dimension 2
You may benefit from looking at: repository.uwyo.edu/cgi/… and perhaps this tiny writeup: arxiv.org/abs/1201.4651 |
Nov 1 |
comment |
The formula for a perhaps basic identity (move from stackexchange)
So in other words, this is $\prod_l\det(P_l)$, where $P_l$ is a diagonal matrix with entries $[1+x_l+y_i]_{i=1}^n$; i.e., $\det(P_1\cdots P_m)$. But expanding out the products seems to not be so cool; perhaps working with $\sum_{kl}\log ...$ may be more helpful. |
Oct 31 |
comment |
Eigenvectors of a particular transition matrix
@darijgrinberg: Good suggestion. I'll spend some time over the weekend to clean up the post, and put the heuristics into the background. Thanks!! |
Oct 31 |
comment |
Eigenvectors of a particular transition matrix
@darijgrinberg: actually, scratch all the other stuff; I remembered that actually $V=\exp(L_n)$ above turns $P^{-1}$ into an upper triangular matrix, from which one can immediately read off the eigenvalues of $P^{-1}$, no need to go over to $P^{-2}$, which I had to do when trying to get the eigenvectors! |
Oct 31 |
comment |
Determinant of a determinant
Would be interesting if we could exploit the usual (complex field) fact that $\det(A)=\wedge^n A$, and the block-matrix lemma mentioned here: mathoverflow.net/questions/173088/… by extracting wedge products of individual blocks as principal submatrices of the wedge products of the entire matrix (these relations don't seem to depend on having a field) |
Oct 29 |
comment |
Product $PVPVP$ is elementwise nonnegative?
@cardinal: please excuse my slowness, but is it then immediate that one gets elementwise nonnegativity? |
Oct 28 |
answered | Minimize distance between centroids of subsets of points |
Oct 28 |
reviewed | Close Determinant of block covariance matrix |
Oct 28 |
comment |
Cauchy matrices with elementary symmetric polynomials
Unfortunately, this question has seems to have a negative answer (as proved to me very recently by one of the mathematicians with whom I discussed it; will update this question once I get a chance.) |
Oct 28 |
awarded | matrices |