## Involuntary

A Linear Transformation of period two. Since a Linear Transformation has the form,

 (1)

applying the transformation a second time gives
 (2)

For an involuntary, , so
 (3)

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

The first equation gives . Taking would require , giving , the identity transformation. Taking gives , so
 (7)

the general form of an Involution.