We consider -shearing matrices
-
with
.
The condition for some
to be an
eigenvalue
means
-
This yields the equations
-
For
,
we get
and hence also
,
that is, only can be an eigenvalue. In this case, the second equation is fulfilled, and the first equation becomes
-
For
,
we get
and thus is the eigenspace for the eigenvalue , and is an eigenvector which spans this eigenspace. For
,
we have the identity matrix, and the
eigenspace
for the eigenvalue is the total plane.