English

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

Rings and Algebras 2019-06-06 v1

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.

Keywords

Cite

@article{arxiv.1906.01918,
  title  = {The Jordan-Chevalley decomposition and Jordan canonical form of a quaternionic linear operator},
  author = {Han Gang and Yu Jing and Sun Zheyu},
  journal= {arXiv preprint arXiv:1906.01918},
  year   = {2019}
}