are orthogonal.
Orthogonal 
matrices can all be written as a rotation matrix
or as the product of a rotation matrix by a reflexion 
.
This proves the statements of section 3.1.
Proof: Being a symmetric and positive semi-definite matrix
can always be diagonalised as:
One can look for a matrix 
such that
If 
as a non zero determinant, can be obtained as:
It is easy to see that is orthogonal using Eq. (27) and the fact the inverse
of an orthogonal matrix is obtained by transposition:
which proves Eq. (26).
If the Jones matrix as a zero determinant, as is the case for a
perfect polariser, it means that there is a direction in the
incoming polarisation space, indexed by a unit vector |n> such that
. In the orthogonal direction |m> the action of
is 
, where |m'> is a unit vector defining
a direction of the outgoing polarisation space (and
|n'> the orthogonal one). Then can be written as:
which is Eq. (26) ( |i>, |j> and |i'>, |j'> are
orthonormal basis vectors in the incoming and outgoing polarisation
spaces).