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location  Pisa, Italy  
age  31  
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Numerical linear algebra. Mainly matrix equations and their applications (control theory, applied probability).
2h

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How to transform matrix to this form by unitary transformation?
"Notice that UMV still has spectral radius $m_1$"  why? The singular values are preserved, but the spectrum may change. 
Apr 15 
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Trace of Inverse matrix from Cholesky
Oh, and for a SPD matrix, essentially the eigendecomposition is the SVD. 
Apr 15 
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Trace of Inverse matrix from Cholesky
What about computing an upper triangular Cholesky factor instead? Then, from the shape of $\Sigma^{1}=U^{T}U^{1}$, you get that the diagonal entries are the squares of the inverse of the diagonal of $U$. 
Apr 8 
reviewed  Reject suggested edit on Generalized Radon transform (Relaxed sufficient condition for invertibility) 
Apr 5 
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Approximate the square root of (1X) efficiently through (nested) products
@DehuaCheng I see. Don't you have the same problem in your example with $(IX)^{1}$, then? If you expand out all the products, it becomes $2^d$ operations again. 
Apr 4 
answered  Approximate the square root of (1X) efficiently through (nested) products 
Apr 3 
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Complexity of turning a ddegree polynomial to 2degree polynomial
Also, your "general polynomial" has a very special form. For that polynomial, you can get rid of the exponent $d$ in the minimum problem, for instance. 
Apr 2 
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Complexity of turning a ddegree polynomial to 2degree polynomial
Your question is not well defined. As it is, one can just set $z:=p(x)x^2$ to get $p(x)=x^2+z$, which has degree 2. 
Apr 2 
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What areas of pure mathematics research are best for a postPhD transition to industry?
I wouldn't define machine learning and mathematical biology "pure mathematics". 
Apr 2 
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NPhard problems in linear algebra and real analysis
Computing the tensor rank is also NPhard. 
Mar 30 
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Does $Mv$ converge to i.i.d in some sense?
There are several different questions here; one is "is each of the $u_i$ separately $Bin(n,1/4)$" (yes), another is "are the $u_i$ independent from each other?" (no, not always, I guess), and a third (if I read between the lines) is "does some result such as a LLN/CLT hold as if they were independent?". Maybe you should try and make the last one more explicit: what kind of properties do you need from them? What is your ultimate goal? 
Mar 29 
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Open source mathematical software.
@KjetilBHalvorsen I am not sure that Geogebra is open source. Its webpage geogebra.org/cms/en/license claims that: (1) Geogebra is open source (2) Geogebra is free of charge for noncommercial use only (3) the Geogebra source code is available under the GPL. As far as I know, (2) is in contradiction with both (1) (per the OSI open source definition) and (3) (per the GPL terms). Strange indeed. 
Mar 27 
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Inserting maple or macaulay script in a paper
The problem is that it's not a question on mathematical writing, but on LaTeX syntax. 
Mar 24 
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Is there an example where the error of GaussLaguerre quadrature does not vanish?
The Runge function $x\mapsto \frac{1}{1+25x^2}$ is the standard example of hardtoapproximate function for the GaussLegendre quadrature in the interval $[1,1]$ (which is exact for integrating polynomials of degree up to $2n1$). My first attempt would be trying a change of variable of some form to take that interval into $[0,\infty]$ and Legendre into Laguerre, but I am not an expert in quadrature myself. 
Mar 23 
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The height of the PerronFrobenius eigenvector
ok thanks now I understand better. 
Mar 23 
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The height of the PerronFrobenius eigenvector
probably you misunderstood me; I do know what an eigenvector is, I was asking you to clarify the definition of height, as you did (thanks!). I take it that there should be a similar definition of height or "smallness" for matrices then? What is it if it's not that matrix norm? 
Mar 23 
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The height of the PerronFrobenius eigenvector
I am not familiar with the concept of height and I cannot make sense of your definition on the eigenvector. Could you please formalize it? For the height of the matrix, what you defined is called infinitynorm of a matrix, $\A\_{\infty}$, in matrix analysis (see for instance en.wikipedia.org/wiki/Matrix_norm). It satisfies some "typical" inequalities for a norm such as $\Av\\leq\A\\v\$, and one could probably find more results by looking it up with this name. 
Mar 22 
reviewed  Approve suggested edit on symmetric algebra of an ideal and syzygies 
Mar 22 
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Stationary Distribution for Markovlike system?
Shameless selfadvertising: I have studied a similar problem in sciencedirect.com/science/article/pii/S0024379511004484 and dx.doi.org/10.1137/100796765. Our problem comes from modelling Markovian binary trees with multiple states; I wouldn't be surprised if yours has the same origin. Maybe we can reduce one setting to the other with a change of variable of the form $x=\begin{bmatrix}C\\C\\C\end{bmatrix}\pi$ for some $C>0$ (a change of variable that we use in the second paper that I have linked). 
Mar 22 
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Stationary Distribution for Markovlike system?
@Suvrit $\langle \pi, \pi B\rangle$ is not what you think, from the description it should be the Hadamard product. 