I am recently reading about random matrix theory in engineering applications. I come up with the following question. I have been trying to find any references but it doesn't help. Hopefully, anyone can give me any reference or suggestion to approach this question.
Does Bernoulli random matrix belong to the rotationally-invariant random ensemble?
Where a random matrix $\mathbf{A} \in \mathbb {R}^{m \times n}$ is called a Bernoulli random matrix if its entry $A_{ij}$ is independent and is either $+1$ or $-1$ with equal probability. A random matrix $\mathbf{A}\in \mathbb {R}^{m \times n}$ is called rotationally-invariant if it satisfies $P(\mathbf{A}) = P(\mathbf{U}\mathbf{A}\mathbf{V^T})$, where $\mathbf{U}$ and $\mathbf{V}$ are deterministic orthogonal matrices.