  An eight dimensional matrix representation of the Maxwell equations for a
linear inhomogeneous medium has been derived earlier based on the
Riemann-Silberstein-Weber vector starting from the equations satisfied by it. A
new eight dimensional matrix representation, related to the earlier one by a
similarity transformation, is deduced starting ab initio from the Maxwell
equations. In this process the Riemann-Silberstein-Weber vector is obtained as
natural basis for the matrix representation of the Maxwell equations. The new
representation has a more advantageous structure compared to the earlier one
from the point of view of applications. In the case of a homogeneous medium it
reduces to a block diagonal form with four two dimensional Pauli matrix blocks
along the diagonal and in the case of a linear inhomogeneous medium it should
be suitable for studying the propagation of electromagnetic waves adopting the
techniques of quantum mechanics.
