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Exercise 5.4.4

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We have

T^{k} (W) \subset T^{k - 1} (T (W)) \subset T^{k - 1} (W) \subset \dots \subset W .

For any $v \in W$ , we know that $g (T) (v)$ is the sum of some elements in $W$ . Since $W$ is a subspace, we know that $g (T) (v)$ is always an element is $W$ .

jephianlin

2011-06-27 00:00

Exercise 5.4.4

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