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Exercise 5.4.35

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Let $v$ is an element in $β_{1}$ . We know that $T (v)$ is a linear combination of $β$ . Since $T (v)$ is in $W_{1}$ , we know that the combination only use elements in $β_{1}$ . The same argument could be applied to each element in $β_{i}$ for each $i$ . So we know the matrix representation of $T$ corresponding to the chosen basis $β$ is

B_{1} \oplus B_{2} \oplus \dots \oplus B_{k} .

jephianlin

2011-06-27 00:00

Exercise 5.4.35

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