Proposition 5

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

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

— Let $E$ be a vector space of finite dimension $n$ over a commutative field $K$ , let $u$ be an endomorphism of $E$ , and let $U$ be its matrix with respect to some basis of $E$ . Then for each integer $m$ with $1 \leq m \leq n$ , the product

d_m(X) = q_1(X) q_2(X) \ldots q_m(X)

of the first

m

similarity invariants of

u

is equal to the gcd of the

m

-th order minors of the matrix

XI, - U

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

Cited by

Remark 4, § 5

Cites

Nothing.