The Jordan-Chevalley decomposition and Jordan canonical form of a quaternionic linear operator

Abstract: We introduce some basic notions and results for quaternionic linear operators analogous to those for complex linear operators. Our main result is to prove the additive and multiplicative Jordan-Chevalley decompositions for quaternionic linear operators, which are related by the exponential map. We also give a new proof of the theorem of Jordan canonical form for quaternionic linear operators, which is intrinsic and takes less computations than the known proofs for square quaternionic matrices.