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feat: Some docs

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jstoobysmith 2024-11-11 11:58:48 +00:00
parent 63fcbf3da7
commit dd8554a080
4 changed files with 9 additions and 3 deletions
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4
HepLean/Lorentz/Weyl/Basic.lean
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@ -274,10 +274,14 @@ def leftHandedAltEquiv : leftHanded ≅ altLeftHanded where
rw [one_mulVec]
rfl
/-- `leftHandedAltEquiv` acting on an element `ψ : leftHanded` corresponds
to multiplying `ψ` by the matrix `!![0, 1; -1, 0]`. -/
lemma leftHandedAltEquiv_hom_hom_apply (ψ : leftHanded) :
leftHandedAltEquiv.hom.hom ψ =
AltLeftHandedModule.toFin2ℂEquiv.symm (!![0, 1; -1, 0] *ᵥ ψ.toFin2ℂ) := rfl
/-- The inverse of `leftHandedAltEquiv` acting on an element`ψ : altLeftHanded` corresponds
to multiplying `ψ` by the matrix `!![0, -1; 1, 0]`. -/
lemma leftHandedAltEquiv_inv_hom_apply (ψ : altLeftHanded) :
leftHandedAltEquiv.inv.hom ψ =
LeftHandedModule.toFin2ℂEquiv.symm (!![0, -1; 1, 0] *ᵥ ψ.toFin2ℂ) := rfl