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refactor: Spelling and typos

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jstoobysmith 2025-02-10 10:51:44 +00:00
parent b30a49d7db
commit dc5b63c4a7
25 changed files with 37 additions and 37 deletions
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8
HepLean/Lorentz/PauliMatrices/SelfAdjoint.lean
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@ -338,7 +338,7 @@ lemma σSAL_decomp (M : selfAdjoint (Matrix (Fin 2) (Fin 2) ℂ)) :
ring
/-- The component of a self-adjoint matrix in the direction `σ0` under
the basis formed by the covaraiant Pauli matrices. -/
the basis formed by the covariant Pauli matrices. -/
@[simp]
lemma σSAL_repr_inl_0 (M : selfAdjoint (Matrix (Fin 2) (Fin 2) ℂ)) :
σSAL.repr M (Sum.inl 0) = 1 / 2 * Matrix.trace (σ0 * M.1) := by
@ -355,7 +355,7 @@ lemma σSAL_repr_inl_0 (M : selfAdjoint (Matrix (Fin 2) (Fin 2) ℂ)) :
simp [σSAL]
/-- The component of a self-adjoint matrix in the direction `-σ1` under
the basis formed by the covaraiant Pauli matrices. -/
the basis formed by the covariant Pauli matrices. -/
@[simp]
lemma σSAL_repr_inr_0 (M : selfAdjoint (Matrix (Fin 2) (Fin 2) ℂ)) :
σSAL.repr M (Sum.inr 0) = - 1 / 2 * Matrix.trace (σ1 * M.1) := by
@ -372,7 +372,7 @@ lemma σSAL_repr_inr_0 (M : selfAdjoint (Matrix (Fin 2) (Fin 2) ℂ)) :
simp [σSAL]
/-- The component of a self-adjoint matrix in the direction `-σ2` under
the basis formed by the covaraiant Pauli matrices. -/
the basis formed by the covariant Pauli matrices. -/
@[simp]
lemma σSAL_repr_inr_1 (M : selfAdjoint (Matrix (Fin 2) (Fin 2) ℂ)) :
σSAL.repr M (Sum.inr 1) = - 1 / 2 * Matrix.trace (σ2 * M.1) := by
@ -389,7 +389,7 @@ lemma σSAL_repr_inr_1 (M : selfAdjoint (Matrix (Fin 2) (Fin 2) ℂ)) :
simp [σSAL]
/-- The component of a self-adjoint matrix in the direction `-σ3` under
the basis formed by the covaraiant Pauli matrices. -/
the basis formed by the covariant Pauli matrices. -/
@[simp]
lemma σSAL_repr_inr_2 (M : selfAdjoint (Matrix (Fin 2) (Fin 2) ℂ)) :
σSAL.repr M (Sum.inr 2) = - 1 / 2 * Matrix.trace (σ3 * M.1) := by