Exercise 5.1.5

Answers

By definition, that $v$ is an eigenvector of $T$ corresponding to $λ$ means $Tv = λv$ and $v \neq 0$ . Hence we get

Tv - λv = (T - λI) v = 0

and $v \in N (T - λI)$ . Conversely, if $v \neq 0$ and $v \in N (T - λI)$ , we have $Tv = λv$ . It’s the definition of eigenvector.

jephianlin

2011-06-27 00:00