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32878
bio website suvrit.de
location MIT
age
visits member for 4 years, 7 months
seen 3 hours ago

Researcher in Optimization and Machine Learning.

Hobbyist in Inequalities, Matrix Analysis, Polynomials, etc.

I'm here mostly to learn mathematics!


15h
reviewed Close How to character the norm of elemental units in a quadratic number field
1d
comment A “quadratic” triangular inequality
@FedorPetrov: perhaps make your comments an answer so that this question attains "answered" status...
Mar
25
comment Represent matrix immanants using Schur functions
Thanks Hari! How about $d_\lambda$ in terms of $s_\lambda$?
Mar
25
comment Represent matrix immanants using Schur functions
@VladimirDotsenko: indeed, the ideal is not attainable, but perhaps a nonnegative sum over sufficient number of suitable "parts"?
Mar
25
comment Represent matrix immanants using Schur functions
In the ideal case, we'd have $d_\lambda(A)$ represented as some combination of Schur functions evaluated at eigenvalues of $A$. E.g., if $\lambda=(1^n)$, $d_\lambda(A)=\det(A)=s_\lambda(a_1,\ldots,a_n)=\prod_i a_i$ ... also, I looked at "Littlewood's correspondence principle" but could not get something simple out of it.
Mar
25
asked Represent matrix immanants using Schur functions
Mar
24
answered Automatically generate BibTeX item from arxiv
Mar
23
comment Geometric interpretation for partial trace?
In other words, if $A=X \otimes Y$ is tensor product of density matrices, then $\text{tr}_2(A)=X$ and $\text{tr}_1(A)=Y$ (this is the marginalizing out that Carlo mentioned).
Mar
20
revised Smallest eigenvalue of a tricky random matrix
Fixed image that had disappeared due to imageschack having removed it...
Mar
20
comment Finding the optimal mixture of two convex functions
Trying doing alternating minimization (which exploits exactly what you wrote in the post); fix $x_1,x_2$ minimize over $p$, then fix $p$ and optimize over $x_1$, $x_2$ and iterate.
Mar
20
comment Matrix inequality
@mikitov: this is somewhat standard in matrix analysis, so I would at best say: "We thank Mathoverflow (linking to this post) for bringing to our attention a standard result that helps...."
Mar
19
awarded  Inquisitive
Mar
19
answered Matrix inequality
Mar
19
comment What are interesting heuristics of determining how far given matrix is from a singular one?
You should search for: "numerical rank"
Mar
17
comment Monotonicity of a ratio of conditional expectation operator
I asked, because it is not clear from the outset, where would the fact that $T$ is a conditional expectation operator play a role for monotonicity --- it seems to be used mostly for the contractivity. On the other hand, even non-contractive operators can lead to a monotonic ratio, so maybe your hypothesis does play a role...
Mar
17
comment Monotonicity of a ratio of conditional expectation operator
Does this monotonicity break for an arbitrary contractive operator?
Mar
13
comment What are good bounds on ratios of subdeterminants?
You can also use convexity of this function to get some bounds.
Mar
12
comment The Maximal $\ell_2$ norm of a signed sum of vectors
@KZH Please see my comment to Igor's answer. The google keyword "maxqp charikar" will bring up the relevant search results.
Mar
12
comment The Maximal $\ell_2$ norm of a signed sum of vectors
As I also mentioned in my comments, this problem in the exact incarnation of the OP also goes under the name MaxQP in the theory CS literature, and has been the subject of fairly intense study (it contains the MaxCUT problem as a special case), including bounds obtained from Grothendieck's inequality, etc.
Mar
12
comment The Maximal $\ell_2$ norm of a signed sum of vectors
Duh, wasn't this already closed? Did you look at MaxQP (that was in my last comment)...