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

Also, how is this fact related to invariant subspaces?

- Dec 14th 2009, 08:19 PMcubrikalAny polynomial is the characteristic polynomial of some linear operator?
Why is it that any polynomial of degree n with leading coefficient $\displaystyle (-1)^n$ the characteristic polynomial of some linear operator?

Also, how is this fact related to invariant subspaces? - Dec 15th 2009, 07:26 AMtonio