Remark 3

Tag 0775, permanent. Cite it as [Bourbaki, Tag 0775].

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

The notion of Jordan decomposition for a square matrix can be defined in an analogous manner. For example, for the Jordan matrix $U_{m,\alpha}$ we have

(U_{m,\alpha})_s = \alpha \cdot I_m , \quad (U_{m,\alpha})_n = U_{m,0} .

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

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