bio  website  suvrit.de 

location  Internet  
age  
visits  member for  4 years, 9 months 
seen  2 hours ago  
stats  profile views  9,152 
Researcher in Optimization and Machine Learning.
Hobbyist in Inequalities, Matrix Analysis, Combinatorics, Algebra, etc.
I'm here mostly to learn mathematics!
3h

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The sum of squared logarithms conjecture
Oh I did not realize that the paper I saw two years ago was by you and your coauthors! I hope MO helps prove it. 
8h

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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 (Emajorization is just the majorization in terms of elementary symmetric functions as noted in the conjecture above) 
8h

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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 finegrained description of the spectrum seems too hard. 
11h

answered  Hadamard Product and Eigendecomposition 
11h

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Hadamard Product and Eigendecomposition
the obvious answer is: no there won't be a nontrivial closed form. 
22h

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An inequality for copulas
Quite an interesting question. Once I get some time, I'll think about it again. I'm hoping that the Laplace transform representation helps achieve the proof... 
2d

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An inequality for copulas
My answer establishes the claim for $t \ge 1$. So I guess the question is now for general CM $f$... 
May 25 
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Concavity of mixed volumes and mixed discriminants
Ok, that clarifies my doubts. Before plowing into this, however, I'd like to ask you do you have any numerical evidence that suggests that your conjecture may hold? Thanks! 
May 25 
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Solving nonlinear inequality that involves norm2 operator
It is not clear what is it that you are trying to solve. What you have written is an inequality, not an equation. In particular, since $C, q, Z, p$ are all fixed, I don't see why making $\psi \to 0$ will not solve the inequality. I must be missing something... 
May 25 
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Concavity of mixed volumes and mixed discriminants
The closest paper I found relevant to your question is: arxiv.org/pdf/1412.8200.pdf  does Corollary 4.1 in there help? 
May 25 
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Concavity of mixed volumes and mixed discriminants
The discussion on pg. 391 of ams.org/journals/bull/20023903/S0273097902009412/… seems to contain useful pointers; the conjecture seems nice but probably it breaks. 
May 25 
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John Nash's Mathematical Legacy
I hope somebody with more expertise chimes up and summarizes Nash's work on cooperative games (I had the fortune to attend a talk by him in 2008 where he carefully described his cooperative games model, he almost expressed a personal relation with each of the variables on his slides)... 
May 24 
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Solving nonlinear inequality that involves norm2 operator
the question is not clear; what about $\psi=0$? 
May 20 
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complexity of eigenvalue decomposition
@SébastienLoisel: I think you are right to worry about the true computational complexity; I am not sure if the paper I linked to manages to avoid intermediate coefficient growth  so your skepticism is justified... 
May 20 
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complexity of eigenvalue decomposition
@IgorRivin: no, as also Robert notes, the unitary eigenproblem is as easy/hard as the general case (so it can be done in $O(n^3)$. 
May 19 
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complexity of eigenvalue decomposition
Please have a look at the paper: "The complexity of the matrix eigenproblem" by Victor Pan and Zhao Chen. Their Theorem 1 contradicts your claims... 
May 15 
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Sum identities with immanants
That result is an adaptation of en.wikipedia.org/wiki/Schur_orthogonality_relations  so that in particular, if $G$ is a finite group and $\chi, \xi$ are irreducible chars, then $$\sum_{\sigma \in G} \overline{\chi(\sigma)}\xi(\sigma\tau) = \begin{cases} G\chi(\tau)/\chi(e), & \text{if}\ \chi=\xi;\\ 0 & \text{otherwise}.\end{cases}$$ 
May 15 
answered  Sum identities with immanants 
May 13 
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Convexity of the product of two exponential matrices
Although the original claim is false (Mike Jury has an excellent explicit counterexample), a much weaker related claim is true. Claim. Let $A \in M_n(\mathbb{C})$. The function $f: [0,c] \to \mathbb{R}_+$ defined by \begin{equation*} f(t) = \e^{tA}\ \end{equation*} is convex for any unitarily invariant norm $\\cdot\$. 
May 12 
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$\int_0^\infty x \, [J_0(x)]^5 \, dx$: source and context, if any?
More generally, also directly relevant are pp. 419421 of Watson's "Treatise on Bessel functions" 