Definition 4

Tag 075Z, permanent. Cite it as [Bourbaki, Tag 075Z].

An endomorphism satisfying conditions (i), (ii) and (iii) of Prop. 8 is called triangularisable.

In particular if $K$ is algebraically closed, then every endomorphism of a $K$ -vector space is triangularisable.

For matrices, Prop. 8 implies :

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

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