Involutory

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.