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Exercise 7.2.16

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Since the eigenvalue is zero now, observe that if $x$ is an element in $β$ corresponding to one dot called $p$ , then $T (x)$ would be the element corresponding to the dot just above the dot $p$ . So the set described in the exercise is an independent set in $R (T^{i})$ . By counting the dimension of $R (T^{i})$ by Theorem 7.9, we know the set is a basis for $R (T^{i})$ .

jephianlin

2011-06-27 00:00

Exercise 7.2.16

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