Exercise 8.C.11

Answers

Proof. Let $z^{m} + \dots + a_{1} z + a_{0}$ be the minimal polynomial of $T$ . Then

a_{0} I = - T^{m} - \dots - a_{1} T

Multiplying both sides of the equation above by $\frac{1}{a_{0}} T^{- 1}$ gives the desired result (note that $a_{0}$ is nonzero by Exercise 8). □

celiopassos

2017-10-06 00:00