Before revision:  For decomposing flows H\!K {\cal  _A(t), the algorithm decomposes the given dense general matrix A unitarily into  U^*AU = \text { diag} (A_j) with  diagonal blocks A_j that conform in size with those of H\!K_A .
After revision:  For decomposing flows H\!K {\cal _A(t), the algorithm decomposes the given dense general matrix A unitarily into block-diagonal form U^*AU = \text { diag} (A_j) with diagonal blocks A_j that conform in size with those of H\!K_A .