Corollary 1

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

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

— Let K be a field, let E and $E'$ be two finite dimensional vector spaces over K, and let u (resp. $u'$ ) be an endomorphism of E (resp. $E'$ ). Then u and $u'$ are similar (VII, p. 29) if and only if they have the same similarity invariants.

Indeed $u$ and $u'$ are similar if and only if the $K[X]$ -modules E, and $E'_u$ are isomorphic.

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

Cited by

Corollary 2, § 5

Cites

Nothing.