(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.