Littlewood's algorithm and quaternion matrices

AbstractA strengthened form of Schur's triangularization theorem is given for quaternion matrices with real spectrum (for complex matrices it was given by Littlewood). It is used to classify projectors (A2=A) and self-annihilating operators (A2=0) on a quaternion unitary space and examples of unitarily wild systems of operators on such a space are presented. Littlewood's algorithm for reducing a complex matrix to a canonical form under unitary similarity is extended to quaternion matrices whose eigenvalues have geometric multiplicity 1