Littlewoodʹs algorithm and quaternion matrices Original Research Article

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