# Math Help - Any polynomial is the characteristic polynomial of some linear operator?

1. ## Any polynomial is the characteristic polynomial of some linear operator?

Why is it that any polynomial of degree n with leading coefficient $(-1)^n$ the characteristic polynomial of some linear operator?

Also, how is this fact related to invariant subspaces?

2. Originally Posted by cubrikal
Why is it that any polynomial of degree n with leading coefficient $(-1)^n$ the characteristic polynomial of some linear operator?

Also, how is this fact related to invariant subspaces?