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Numerical linear algebra. Mainly matrix equations and their applications (control theory, applied probability).
2d

reviewed  Approve suggested edit on R is regular local rings of Krull dimension 2.Can we find any ideal of height 2 different from m? 
2d

comment 
Basis for the rational functions
@VladInfinitum It is difficult to answer without knowing your specific needs, and I am not an expert on the topic. I suggest you to look at an introductory book such as Geometric Modeling with Splines: An Introduction, Cohen, Rosenfeld, Elber, or at least take a look around on Wikipedia (Splines, BSplines, NURBs, Spline interpolation). 
2d

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Basis for the rational functions
Actually rational functions aren't used very often in numerical analysis as a modelling tool. Splines (spaces of piecewise polynomials or rational functions, with compactlysupported bases) and their variants are more popular. 
Jul 21 
reviewed  Approve suggested edit on noncommutativegeometry tag wiki 
Jul 21 
reviewed  Approve suggested edit on noncommutativegeometry tag wiki excerpt 
Jul 21 
revised 
a book comparable to Development of mathematics in the 19th century by F.Klein?
grammar 
Jul 16 
comment 
Recommendations for symmetric preconditioner
I'd suggest asking this on scicomp.stackexchange.com  the community there is more expert in numerical methods; MO is more oriented towards nonapplied mathematics. Please flag your question for moderation attention to suggest migration if you agree. 
Jul 15 
answered  Determinant of sum of Kronecker products 
Jul 15 
comment 
LU factorization for $I+A$ (A skewsymmetric)
I would be very careful in assuming this is true based on numerical examples only. The worstcase bounds for the growth factor in LU factorization of general (nonantisymmetric) matrices are quite hard to reach in practice. 
Jul 14 
reviewed  Approve suggested edit on Proof or citation? 
Jul 4 
reviewed  Reject suggested edit on Is there a coordinate free proof of the MorreyKohnHormander identity? 
Jul 4 
comment 
Generalising the cyclic property of the trace of a matrix
By the way, Peter Semrl has characterized the linear maps from $C^{n\times n}$ to itself that preserve many different properties, including those that [preserve similarity](www.fmf.unilj.si/~semrl/preprints/similarity.pdf). This problem looks related. 
Jul 4 
comment 
Generalising the cyclic property of the trace of a matrix
Other semitrivial examples of functions with the cyclic property, but without the other ones that you ask for, are the $\ell^p$norms of the eigenvalues. 
Jul 4 
reviewed  Approve suggested edit on if $X$ is a vector field in $\mathbb{R}^3$ and $h$ is a periodic orbit, then $X$ have a singularity? 
Jul 3 
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Matrix equation solving guidelines
$B$ should be $Q\otimes P + Q^T \otimes P^T$, without the $\operatorname{vec}$, isn't it? 
Jul 3 
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Matrix equation solving guidelines
@Mahdi no, the idea works, it is just inefficient if the OP has practical solution in mind, and it seems to me that the algebra in your post is still incorrect. Please do not take the downvote as a personal thing. 
Jul 3 
answered  Matrix equation solving guidelines 
Jul 2 
awarded  Curious 
Jun 27 
reviewed  Reject suggested edit on Is the Szego projection on a codim$k$ CR manifold an integral operator? 
Jun 27 
reviewed  Approve suggested edit on $6$ points lie on a conic if and only if $ABC$ and $A_0B_0C_0$ are perspective 