Exercise 8.C.8

Answers

Proof. Let $p$ denote the minimal polynomial of $T$ . We have

\begin{aligned} T is invertible & ⟺ 0 is not an eigenvalue of T \\ ⟺ p (0) \neq 0 \\ ⟺ the consant term of p is nonzero, \end{aligned}

where the equivalence between the first and second lines follows from 8.49. □

celiopassos

2017-10-06 00:00