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Any unitary matrix $U$ can be diagonalized by another unitary matrix $V$, $$U=VDV^\dagger,$$ where $D={\rm diag}(z_1,z_2,...,z_N)$ is diagonal. If $U$ is taken at random uniformly with respect to Haar ...

After the uniform distribution (normalized Haar measure), the matrix Fisher distribution seems to be the most popular probability distribution on the Lie group SO(3). The density is proportional to ...