feynlag.vacuum.diagonalize.solve_mixing_angle_2x2¶

feynlag.vacuum.diagonalize.solve_mixing_angle_2x2(M, positive_denominator=True)[source]¶

Mixing angle of a real symmetric 2×2 matrix from the off-diagonal condition (R M Rᵀ)₁₂ = 0: tan 2θ = 2 M₁₂ / (M₁₁ − M₂₂).

Returns:: (theta, tan2theta) — the angle θ = ½ atan(...) and the defining tan 2θ expression (keep it: CONVENTIONS.md requires verifying any rotation angle against its tan-2θ source).