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Let $\mathbf{x} \in \mathbb{C}^M$ is an unknown distributed random vector (certainly not gaussian), and matrix $\mathbf{A}\in \mathbb{C}^{M \times M}$ which is fix (known). Also, assume we know the ...

Consider an arbitrary finite set of orthogonal-projection matrices (symmetric, idempotent, etc.) in $\mathbb{R}^{n\times n}$. We draw two matrices $Q,P$ uniformly and i.i.d. from this set. Question: ...

I want to ask a question regarding the invariance of determinants under permutation. The following matrix is the one I want to discuss here. (It's just a symmetric block tridiagonal matrix with non-...

I want to compute the following expectation term: $E[{\bf{XA}}{{\bf{X}}^T}]$ where ${\bf X} \in R^{M \times M}$ and its elements are normal random variables such that $vec\left( {\bf{X}} \right)\...

We define $T: C[0,1]\to C[0,1]\ni T(f(x))= \sum\limits_{k=1}^{m} p_k (f\circ f_k)(x):=\mathbb E( f(X_{n+1}|X_n=x)$ for a system $X_{n+1}=f_{\omega_n}(X_n), n=0,1,2\dots.$ and $\omega_n$ are i.i.d ...