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 Yearling
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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