Abstract
A 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 ( A 2= A ) and self-annihilating operators ( A 2=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.
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