Assume $G$ is a member of the GiOE (GiUE). I sample a Haar-random unitary matrix $U$ and multiple the two, either like $G \cdot U$ or $U \cdot G$. Would it be correct to say that the GiOE (GiUE) is invariant under this operation?
2026-03-02 17:13:59.1772471639
Multiplication (left or right) of Ginibre Orthogonal (GiOE) or Unitary (GiUE) with a Haar-random unitary matrix
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