Noted by @izaid here: https://github.com/numpy/numpy/issues/24451#issuecomment-1684321328 `U^H` should come before `U`. Example of discrepancy with the SciPy docs: https://docs.scipy.org/doc/scipy/reference/generated/scipy.linalg.cholesky.html. The SciPy version is consistent with other material I have found online. 