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

• Dec 14th 2009, 08:19 PM
cubrikal
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?
• Dec 15th 2009, 07:26 AM
tonio
Quote:

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?