Corollary 1
Tag 07ZT, permanent. Cite it as [Bourbaki, Tag 07ZT].
Topological Vector Spaces, V, p. 24, § 2. Orthogonal families in a hilbertian space
Given two orthonormal bases in a hilbertian space E, there exists an automorphism of E transforming the first basis into the second.
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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