Find the minimal polynomial given where
I found the associated matrix, which is
Now I need to compute the characteristic polynomial, and this is
Now suppose I take then I make if this is zero, then that polynomial is the minimal one right? If is not zero, then I consider the characteristic polynomial, and that's actually the minimal polynomial because of simple application of Cayley - Hamilton Theorem.
== Yup, but in fact it's easier: since the minimal and the char. polynomials have the same irreducible factors, you know the min. pol. = the char. pol. in this case!
Another question I have, suppose we're computing the characteristic polynomial, when is it equal to the minimal one?
There's not easy way to say.