Corollary 4

Tag 0772, permanent. Cite it as [Bourbaki, Tag 0772].

Algebra, chapter VII, § 5. Endomorphisms of vector spaces

Suppose $u$ has a Jordan decomposition, and let R be a polynomial in $\mathbf{K}[X]$ . Then the endomorphism $R(u)$ has a Jordan decomposition with $R(u)_s = R(u_s)$ .

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

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