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feat: General properties of contractions

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jstoobysmith 2024-11-18 15:42:37 +00:00
parent dcf6b774d4
commit 9b4cd5d0b8
10 changed files with 366 additions and 269 deletions
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HepLean/Lorentz/RealVector/Contraction.lean
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@ -421,7 +421,7 @@ lemma on_basis (μ ν : Fin 1 ⊕ Fin d) : ⟪ContrMod.stdBasis μ, ContrMod.std
mul_zero, off_diag_zero]
lemma matrix_apply_stdBasis (ν μ : Fin 1 ⊕ Fin d) :
Λ ν μ = η ν ν * ⟪ ContrMod.stdBasis ν, Λ *ᵥ ContrMod.stdBasis μ⟫ₘ := by
Λ ν μ = η ν ν * ⟪ContrMod.stdBasis ν, Λ *ᵥ ContrMod.stdBasis μ⟫ₘ := by
rw [on_basis_mulVec, ← mul_assoc]
simp [η_apply_mul_η_apply_diag ν]