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 Jan 31 comment Distribution of Product of Matrices holding Multivariate Random Normal Variable Observations It's still not clear what are those distributions? Are they distributions for the columns (or rows) of $A$ and $B$ or something else? A vectorization simply mean to put the entries if the matrix in a vector (column-wise or row-wise). By the way, I doubt that you can find a simple distribution for the general case. However, you might be able to say something about the general behavior of those product matrices , depending on the assumptions made. Jan 31 comment Distribution of Product of Matrices holding Multivariate Random Normal Variable Observations Clarify if the columns or the rows have the given distributions? or the vectorized matrix has those distributions? If the columns (or rows) have the given distributions are they independent? Jan 13 comment How to calculate explicitly Cheeger constant (also caled Cheeger number or Isoperimetric number)? For a generic graph there's no computationally efficient method to compute the constant. See here. Jan 8 comment About the Alon-Krivilevich-Vu result on concentration of eigenvalues of random matrices. Think of the median as the fixed threshold for which the probability of the random variable exceeding the threshold is 1/2. The tail bounds you are referring to are some form of concentration inequalities. In general, they say that a random variable is most of the time within a small neighborhood of its median (or mean). Oct 29 revised Efron-Stein inequality for chi distributed random variables added 13 characters in body Oct 28 asked Efron-Stein inequality for chi distributed random variables Sep 9 comment Eigenvalues of real symmetric matrix @LSB.user255259 You can simply take $B$ as the counter example. You can find the eigenvalues of $B$ explicitly. Sep 9 comment Eigenvalues of real symmetric matrix @AlgebraicPavel If $\rho$ denotes the spectral radius, I think $\rho(B)=n-1$ (assuming $n>1$). Jul 13 awarded Yearling Jun 24 revised Concentration inequality of weighted sum of random variables given a tail inequality a second attempt is explained May 14 comment Why does $\frac{\textbf{g}^T\textbf{d}}{\textbf{d}^T\textbf{H}\textbf{d}}$ give the maximum of function $\mathcal{D}(\textbf{x}+\lambda\textbf{d})$ It's fine. You can simply add a sentence in the end titled update or edit and mention what was your mistake. May 14 comment Why does $\frac{\textbf{g}^T\textbf{d}}{\textbf{d}^T\textbf{H}\textbf{d}}$ give the maximum of function $\mathcal{D}(\textbf{x}+\lambda\textbf{d})$ I think it is fine the way it is. However, it would have been better if you made your corrections in a way that people can see that the question is corrected/modified. May 14 comment Why does $\frac{\textbf{g}^T\textbf{d}}{\textbf{d}^T\textbf{H}\textbf{d}}$ give the maximum of function $\mathcal{D}(\textbf{x}+\lambda\textbf{d})$ Yes, that's it. May 14 comment Why does $\frac{\textbf{g}^T\textbf{d}}{\textbf{d}^T\textbf{H}\textbf{d}}$ give the maximum of function $\mathcal{D}(\textbf{x}+\lambda\textbf{d})$ They denote what you get from the Newton's formula $\lambda^+$ rather than $\lambda^*$. They first find the unconstrained maximum which is $\lambda^+$, and then check if it is in the interval $\Lambda$. If it is in the interval the $\lambda^*=\lambda^+$ otherwise $\lambda^*$ is at one of the endpoints of $\Lambda$. Jan 15 revised The relation between $\inf_{R\in \mathsf{U}_n} \left\Vert A - BR\right\Vert^2_F$ and $\left\Vert AA^*-BB^*\right\Vert$ corrected little errors in math Jan 14 revised The relation between $\inf_{R\in \mathsf{U}_n} \left\Vert A - BR\right\Vert^2_F$ and $\left\Vert AA^*-BB^*\right\Vert$ edited title Jan 14 revised The relation between $\inf_{R\in \mathsf{U}_n} \left\Vert A - BR\right\Vert^2_F$ and $\left\Vert AA^*-BB^*\right\Vert$ edited body; edited title Jan 14 asked The relation between $\inf_{R\in \mathsf{U}_n} \left\Vert A - BR\right\Vert^2_F$ and $\left\Vert AA^*-BB^*\right\Vert$ Dec 21 awarded Constituent Dec 8 awarded Caucus