The inverse of the operator O ^ ^ ⁡ ⁡ , i.e., in E = O ^ ^ − − 1 ⁡ ⁡ J (which requires a specification of the boundary conditions at infinity in a lossless system), has the same symmetry as O ^ ^ and is essentially a Green's function convolution. So, another perspective on Lorentz reciprocity is that it reflects the fact that convolution with the electromagnetic Green's function is a complex-symmetric (or anti-Hermitian, below) linear operation under the appropriate conditions on ε and μ. More specifically, the Green's function can be written as G n m ( x ′ , x ) giving the n -th component of E at x ′ from a point dipole current in the m -th direction at x (essentially, G gives the matrix elements of O ^ ^ − − 1 ), and Rayleigh-Carson reciprocity is equivalent to the statement that G n m ( x ′ , x ) = G m n ( x , x ′ ) . Unlike O ^ ^ ⁡ ⁡ , it is not generally possible to give an explicit formula for the Green's function (except in special cases such as homogeneous media), but it is routinely computed by numerical methods.