One case in which ε is not a symmetric matrix is for magneto-optic materials, in which case the usual statement of Lorentz reciprocity does not hold (see below for a generalization, however). If we allow magneto-optic materials, but restrict ourselves to the situation where material absorption is negligible, then ε and μ are in general 3×3 complex Hermitian matrices. In this case, the operator 1 μ μ ( ∇ ∇ × × ∇ ∇ × × ) − − ω ω 2 c 2 ε ε is Hermitian under the conjugated inner product ( F , G ) = ∫ ∫ F ∗ ∗ ⋅ ⋅ G d V , and a variant of the reciprocity theorem still holds: − − ∫ ∫ V [ J 1 ∗ ∗ ⋅ ⋅ E 2 + E 1 ∗ ∗ ⋅ ⋅ J 2 ] d V = ∮ ∮ S [ E 1 ∗ ∗ × × H 2 + E 2 × × H 1 ∗ ∗ ] ⋅ ⋅ d A where the sign changes come from the 1 i ω ω in the equation above, which makes the operator O ^ ^ anti-Hermitian (neglecting surface terms). For the special case of J 1 = J 2 , this gives a re-statement of conservation of energy or Poynting's theorem (since here we have assumed lossless materials, unlike above): The time-average rate of work done by the current (given by the real part of − − J ∗ ∗ ⋅ ⋅ E ) is equal to the time-average outward flux of power (the integral of the Poynting vector). By the same token, however, the surface terms do not in general vanish if one integrates over all space for this reciprocity variant, so a Rayleigh-Carson form does not hold without additional assumptions.