Plain-language statement
The matrix reps of φ and f φ agree.
Exact Lean statement
lemma toMatrix_f
(φ : FiniteAdeleRing (𝓞 K) K ⊗[K] B ≃L[FiniteAdeleRing (𝓞 K) K]
FiniteAdeleRing (𝓞 K) K ⊗[K] B) :
LinearMap.toMatrix (bGlobal K B) (bGlobal K B) φ.toLinearEquiv
= LinearMap.toMatrix' (f K B φ)Formal artifact
Lean source
lemma toMatrix_f (φ : FiniteAdeleRing (𝓞 K) K ⊗[K] B ≃L[FiniteAdeleRing (𝓞 K) K] FiniteAdeleRing (𝓞 K) K ⊗[K] B) : LinearMap.toMatrix (bGlobal K B) (bGlobal K B) φ.toLinearEquiv = LinearMap.toMatrix' (f K B φ) := by have basis_eq_global' {w : Module.Free.ChooseBasisIndex K B → (FiniteAdeleRing (𝓞 K) K)} : ∑ (j : Module.Free.ChooseBasisIndex K B), (w j) • bGlobal K B j = (ContinuousLinearEquiv.chooseBasisPiScalarRight' K (FiniteAdeleRing (𝓞 K) K) B).symm w := basis_eq_global K B ext simp [f, ← basis_repr_eq_global K B, ← basis_eq_global', LinearMap.toMatrix_apply]- Project
- Fermat's Last Theorem
- License
- Apache-2.0
- Commit
- 8dd808888295
- Source
- FLT/HaarMeasure/HaarChar/FiniteAdeleRing.lean:448-461
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