(
linear algebra,
analysis:)
Let
M be a
square matrix. If for some
nonzero vector v and some
scalar m
Mv = mv (
mathematicians call this "
M acting on v by
multiplication", but all it means is that we take the
matrix product of
M and v) then m is called an
eigenvalue (or "
self value") of
M.
The case is important, because it means that the linear transformation M merely acts as an expansion in the direction of v.