On latently real matrices and block quaternions

Let a complex n × n matrix A be unitarily similar to its entrywise conjugate matrix $\bar{A}$. If in the relation $\bar{A} = {P^*}AP$ the unitary matrix P can be chosen symmetric (skew-symmetric), then A is called a latently real matrix (respectively, a generalized block quaternion). The differences in the systems of elementary divisors of these two matrix classes are found that explain why latently real matrices can be made real via unitary similarities, whereas, in general, block quaternions cannot. Bibliography: 5 titles.