Let
-
be an
endomorphism
on a
finite-dimensional
-vector space
, and let
be an
eigenvector
for with
eigenvalue
.
Let
-
be the
dual mapping
of . We consider bases of of the form with the dual basis . Give examples of the following behavior.
a) is an eigenvector of with the eigenvalue independent of .
b) is an eigenvector of with the eigenvalue with respect to some basis , but not with respect to another basis .
c) is for no basis an eigenvector of .