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The Jordan-Chevalley decomposition and Jordan canonical form of a quaternionic linear operator (1906.01918v1)
Published 5 Jun 2019 in math.RA
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.