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A short constructive proof of Jordan's decomposition theorem

Pawel Kroeger
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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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Pawel Kroeger. 2003-12-29. A short constructive proof of Jordan's decomposition theorem. https://arxiv.org/abs/math/0312041

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