Possible Duplicate:
“Eigenrotations” of a matrix
have a question:
If a matrix $M$ acts by stretching a vector $x$ not changing its direction, then $x$ is an eigenvector of $M$.
Is there a complementary definition if $M$ acts on a vector $X$ not changing its magnitude (but changing its direction)?
Or are they considered equivalent definitions? It seems that we should be able to consider $x$ as an eigenvector in both cases.