(

linear algebra,

analysis:)

Let

**M** be a

square matrix. If for some

nonzero vector v and some

scalar m

**M**v = 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.