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Statistics of spectral properties of matrix-valued random variables.

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Random rotation of a set of distinct points in $\mathbb{R}^n$ [closed]

Consider a set $\{\mathbf{X}_1,\cdots , \mathbf{X}_M\}$ of distinct points in $\mathbb{R}^n$ with $M$ finite. The $M$ values of the $i$-th coordinate do not all have to be dinstinct. For example, in $ …