A short constructive proof of Jordan's decomposition theorem

2003/12/01 by Pawel Kroeger, Kroeger, Pawel
Mathematics · #15A21 #FOS: Mathematics #History and Overview (math.HO) #Mathematics and Applications #math.HO #msc:15A21

paper · pdf · doi:10.48550/arxiv.math/0312041

2 pages, 3 added references

openalex publication_date 2003/12/01 · arxiv created 2003/12/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Although there are many simple proofs of Jordan's decomposition theorem in the literature (see [1], the references mentioned there, and [2]), our proof seems to be even more elementary. In fact, all we need is the theorem on the dimensions of rang and kernel and the existence of eigenvalues of a linear transformation on a nontrivial finite dimensional complex vector space.

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