(
linear algebra,
analysis:)
Let
M be a
square matrix. If for some
nonzero vector v and some
scalar m
Mv = mv (this is
M "acting on" v by
multiplication) then v is called an
eigenvector (or "
self vector") of
M.
Note that all vectors in the direction of v (tv, for any scalar t) are also eigenvectors of M; but they're not really considered "different" for these purposes.