  We complete the rules of translation between standard complex quantum
mechanics (CQM) and quaternionic quantum mechanics (QQM) with a complex
geometry. In particular we describe how to reduce ($2n$+$1$)-dimensional
complex matrices to {\em overlapping\/} ($n$+$1$)-dimensional quaternionic
matrices with generalized quaternionic elements. This step resolves an
outstanding difficulty with reduction of purely complex matrix groups within
quaternionic QM and avoids {\em anomalous} eigenstates. As a result we present
a more complete translation from CQM to QQM and viceversa.

High Energy Physics - Theory