14,935 reputation
33181
bio website suvrit.de
location Internet
age
visits member for 4 years, 10 months
seen 7 hours ago

Researcher in Optimization and Machine Learning.

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

I'm here mostly to learn mathematics!


Jun
27
awarded  Enlightened
Jun
27
awarded  Nice Answer
Jun
25
comment Prove or disprove a matrix logarithm equation
Here is a link to a paper that answers your "kernel" question in complete detail (the log-Euclidean transform indeed leads to a kernel but at the expense of "killing" the curvature): www2.compute.dtu.dk/~sohau/papers/cvpr2015/feragen_cvpr2015.pdf
Jun
25
comment Prove or disprove a matrix logarithm equation
The Riemannian distance is not negative definite; that is, $\exp(-\gamma d^2(X,Y))$ is not a positive definite function.
Jun
23
awarded  Generalist
Jun
8
reviewed Close arg min_X ||A X B - C||^2, with X diagonal
Jun
8
comment Finding a path through real rooted polynomials
Some pointers (maybe you already know this stuff): it seems that material on "maps that preserve real stability" might be of relevance here; maybe Pólya-Schur multipliers or other related results. My understanding of this material is very sketchy, so I don't have something more concrete to say (I tried to turn the question into one about total positivity, but that appeared even harder, so I did not pursue it further).
Jun
8
comment Is this differential identity known?
I do like this proof (and the other two proofs too). I was just trying to respect Terry's request to instead contribute proofs to his blog post :-)
Jun
7
comment Is this differential identity known?
I thought the purpose was not to ask for more proofs (the OP states so), but to find out if and when the identity has been studied before, and in what context, no?
Jun
7
reviewed Close Finding the distribution of a random variable numerically with sample data?
Jun
6
reviewed Close Sum Of n numbers taken $k$ at a time, where numbers are of form $r\choose k$
May
30
awarded  Nice Answer
May
29
comment The sum of squared logarithms conjecture
Wow indeed! Thanks for linking your PDF.
May
29
answered The sum of squared logarithms conjecture
May
29
comment The sum of squared logarithms conjecture
I think this solution has given me a hint on how to prove the result without complex analysis and using elementary methods; great work Lev! I will type out my solution as a corollary of existing results shortly!
May
28
comment The sum of squared logarithms conjecture
Oh I did not realize that the paper I saw two years ago was by you and your co-authors! I hope MO helps prove it.
May
28
comment The sum of squared logarithms conjecture
This conjecture is a really nice one; I saw it a couple of years ago, but did not yet get time to think about it! In particular, it states that if eigenvalues of a positive definite matrix $X$ are $E$-majorized (to be defined) by those of $Y$, then $d(X,I) \le d(Y,I)$, where $d(\cdot,\cdot)$ is the Riemannian distance on the manifold of positive definite matrices (E-majorization is just the majorization in terms of elementary symmetric functions as noted in the conjecture above)
May
28
comment Hadamard Product and Eigendecomposition
@mikitov: if $B$ is special, then surely one can say more; e.g., if $B=11^T$ :-) One can say more precise things about rougher quantities such as $\|A\circ B\|$ etc., or singular value inequalities, and so on; but a fine-grained description of the spectrum seems too hard.
May
28
answered Hadamard Product and Eigendecomposition
May
28
comment Hadamard Product and Eigendecomposition
the obvious answer is: no there won't be a nontrivial closed form.