91Ó°ÊÓ

If \(T \in F_{n}\) has minimal polynomial \(p(x)\) over \(F\), prove that every root of \(p(x)\), in its splitting field \(K\), is a characteristic root of \(T\).

Prove that a normal transformation is unitary if and only if the characteristic roots are all of absolute value \(1 .\)