A linear transformation of period two. Since a linear transformation has the form,
(1)

applying the transformation a second time gives
(2)

For an involutory, , so
(3)

Since each coefficient must vanish separately,
(4)
 
(5)
 
(6)

Equation (5) requires . Taking in turn requires that , giving , i.e., the identity map, while taking gives , so
(7)

which is the general form of a line involution.