Theorems · Definition · number theory

NumberField.mixedEmbedding.euclidean.stdOrthonormalBasis

(K : Type u_1) →
  [inst : Field K] →
    [inst_1 : NumberField K] →
      OrthonormalBasis (NumberField.mixedEmbedding.index K) ℝ (NumberField.mixedEmbedding.euclidean.mixedSpace K)

An orthonormal basis of the Euclidean mixed space.

Defined in: Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic
Cited by: 2 results in Mathlib
Foundations: Depth 233 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field NumberField

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites18

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Realstatement and proof · cited by 25,697
ENNRealstatement · cited by 9,879
Fieldstatement and proof · cited by 7,404
Complexstatement · cited by 5,565
NumberFieldstatement and proof · cited by 653
NumberField.InfinitePlacestatement and proof · cited by 604
EuclideanSpacestatement · cited by 307
NumberField.InfinitePlace.IsRealstatement and proof · cited by 301
NumberField.InfinitePlace.IsComplexstatement and proof · cited by 272
OrthonormalBasisstatement · cited by 188
Equiv.sigmaEquivProdproof · cited by 47
EuclideanSpace.basisFunproof · cited by 26

Cited by2

Results whose statement or proof uses this declaration.

NumberField.mixedEmbedding.euclidean.volumePreserving_toMixedproof · cited by 2
NumberField.mixedEmbedding.euclidean.stdOrthonormalBasis_map_eqstatement and proof · cited by 1