Bourbaki

Definition 2

Tag 02WH, permanent. Cite it as [Bourbaki, Tag 02WH].

Théories spectrales, chapter IV, § 1. Opérateurs compacts sur un espace hilbertien

With the notations of the corollary, the family (αi)i∈I(\alpha_i)_{i\in I} is the family of singular values of uu, relative to the orthonormal basis (ei)i∈I(e_i)_{i\in I} of the initial space of uu.

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.

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Cites

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Machine translation of the English, by gpt-5-6-mini, gpt-5-mini, gpt-5.4, against glossary version 34. Not checked by a person. That model is a cut down version of the one the rest of this language was written by.