Corollary 1

Tag 09DZ, permanent. Cite it as [Bourbaki, Tag 09DZ].

Integration, chapter VII, § 1. Construction of a Haar measure

— Let K be a commutative locally compact field, E a finite-dimensional vector space over K, and u an endomorphism of the vector space E. Then $\mathrm{mod}_E(u) = \mathrm{mod}_K(\det u)$ .

If u is invertible, this follows from Prop. 15. If u is not invertible then $\det u = 0$ , therefore $\mathrm{mod}_K(\det u) = 0 = \mathrm{mod}_E u$ .

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

Cited by

§ 1. Construction of a Haar measure
Example, § 1
Example 8, § 3

Cites

Prop. 15