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refactor: Spellings

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jstoobysmith 2025-02-08 13:07:54 +00:00
parent 4cd71f5ec6
commit 4a55351b72
33 changed files with 88 additions and 88 deletions
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HepLean/Lorentz/PauliMatrices/SelfAdjoint.lean
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@ -301,7 +301,7 @@ lemma σSAL_span : ⊤ ≤ Submodule.span ℝ (Set.range σSAL') := by
def σSAL : Basis (Fin 1 ⊕ Fin 3) ℝ (selfAdjoint (Matrix (Fin 2) (Fin 2) ℂ)) :=
Basis.mk σSAL_linearly_independent σSAL_span
/-- The decomposition of a self-adjint matrix into the Pauli matrices (where `σi` are negated). -/
/-- The decomposition of a self-adjoint matrix into the Pauli matrices (where `σi` are negated). -/
lemma σSAL_decomp (M : selfAdjoint (Matrix (Fin 2) (Fin 2) ℂ)) :
M = (1/2 * (Matrix.trace (σ0 * M.1)).re) • σSAL (Sum.inl 0)
+ (-1/2 * (Matrix.trace (σ1 * M.1)).re) • σSAL (Sum.inr 0)