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Exercise 5.4.13

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If $w$ is an element in $W$ , it’s a linear combination of

{v, T (v), T^{2} (v), \dots .

So $w = g (T) (v)$ for some polynomial $g$ . Conversely, if $w = g (T) (v)$ for some polynomial $g$ , this means $w$ is a linear combination of the same set. Hence $w$ is an element in $W$ .

jephianlin

2011-06-27 00:00

Exercise 5.4.13

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