The three Pauli spin matrices
σ
i
(
i
=
1
,
2
,
3
)
{\sigma _i}\left ( {i = 1,2,3} \right )
occur in the mechanical, especially quantum mechanical, theory of rotation in three-dimensional space. The three spin matrix exponentials are here defined as exp
(
σ
i
x
)
\left ( {{\sigma _i}x} \right )
, where
x
x
is the independent variable. Transmission matrices can be expressed in terms of spin matrix exponentials, thereby permitting a more systematic treatment of transmission line circuits.