Corollary 5

Tag 00NO, permanent. Cite it as [Bourbaki, Tag 00NO].

Algebra, VIII, p. 402, § 21. Linear Representations of Finite Groups

Suppose that the group G is finite and that K is a commutative field in which $|G| \not= 0$ . Let $\pi$ and $\pi '$ be finite-dimensional linear representations of G. Then $\pi$ and $\pi '$ are isomorphic if and only if for every $g$ in G, the endomorphisms $\pi (g)$ and $\pi '(g)$ have the same characteristic polynomial.

This follows from Corollary 1 of VIII, p. 386.

Bourbaki sets the proof directly after the statement, and the corpus does not separate them, so what is above is the statement and its proof together.

Cited by

§ 21. Linear Representations of Finite Groups

Cites

Corollary 1 of VIII, p. 386