Before revision:  It relies on a matrix flow decomposition method that finds a  block-diagonal flow representation for the  hermitean matrix flow H\!K {\cal  _A(t) = \cos(t) H + \sin(t) K if this is possible.
After revision:  It relies on a matrix flow decomposition method that finds a block-diagonal flow representation for the hermitean matrix flow H\!K {\cal F _A(t) = \cos(t) H + \sin(t) K if this is possible.