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Exercise 2.2.11

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Take ${v_{1}, v_{2}, \dots, v_{k}}$ be a basis of $W$ and extend it to be $β = {v_{1}, v_{2}, \dots, v_{n}}$ , the basis of $V$ . Since $W$ is $T$ -invariant, we have $T (v_{j}) = \sum_{i = 1}^{k} a_{ij} v_{i}$ if $j = 1, 2, \dots, k$ . This means ${({[T]}_{β})}_{ij} = 0$ if $j = 1, 2, \dots, k$ and $i = k + 1, k + 2, \dots, n$ .

jephianlin

2011-06-27 00:00

Exercise 2.2.11

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