Corollary 1

Tag 05NT, permanent. Cite it as [Bourbaki, Tag 05NT].

Algebra, chapter II, § 2. Modules of linear mappings. Duality

Let E be a free A-module with a finite basis; for every basis $(e_t)$ *of E, $(c_E(e_t))$ is the dual basis of the basis $(e_t^*)$ of $E^*$ dual to $(e_t)$ .

In this case it is said that $(e_t)$ and $(e_t^*)$ are two dual bases of one another.

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

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