These quantities are all real. In the theory for bodies at rest, the combinations ( are known as Maxwell's Stresses", are known as the Poynting's Vector, as the electromagnetic energy-density, and L as the Langrangian function.
On the other hand, by multiplying the alternating matrices of f and F, we obtain
and hence, we can put
where by L, we mean L-times the unit matrix, i.e. the matrix with elements
Since here , we deduce that,
and find, since , we arrive at the interesting conclusion
i.e. the product of the matrix S into itself can be expressed as the multiple of a unit matrix — a matrix in which all the elements except those in the principal diagonal are zero, the elements in the principal diagonal are all equal