Theorems · Theorem · number theory

NumberField.basisMatrix_eq_embeddingsMatrixReindex

∀ (K : Type u_1) [inst : Field K] [inst_1 : NumberField K],
  NumberField.basisMatrix K =
    Algebra.embeddingsMatrixReindex ℚ ℂ (⇑(NumberField.integralBasis K) ∘ ⇑(NumberField.equivReindex K))
      (RingHom.equivRatAlgHom K ℂ)

Defined in: Mathlib.NumberTheory.NumberField.EquivReindex
Cited by: 2 results in Mathlib
Foundations: Depth 300 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field NumberField

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Cites24

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

DFunLike.coestatement and proof · cited by 62,936
RingHomstatement and proof · cited by 10,189
Equivstatement · cited by 8,337
Fieldstatement and proof · cited by 7,404
Complexstatement and proof · cited by 5,565
Algebra.algebraMapproof · cited by 4,706
Matrixstatement · cited by 4,303
Module.Basisstatement · cited by 1,477
NumberFieldstatement and proof · cited by 653
Matrix.extproof · cited by 540
NumberField.RingOfIntegersstatement and proof · cited by 413
Module.Free.ChooseBasisIndexstatement · cited by 133

Cited by2

Results whose statement or proof uses this declaration.

NumberField.discr_eq_basisMatrix_det_sqproof · cited by 1
NumberField.det_of_basisMatrix_non_zeroproof · cited by 1