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Exercise 2.2.12

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Let ${v_{1}, v_{2}, \dots, v_{k}}$ and ${v_{k + 1}, v_{k + 2}, \dots, v_{n}}$ be the basis of $W$ and $W^{'}$ respectly. By Exercise 1.6.33(b), we have $β = {v_{1}, v_{2}, \dots, v_{n}}$ is a basis of $V$ . And thus we have

{[T]}_{β} = (\begin{matrix} I_{k} & O \\ O & O \end{matrix})

is a diagonal matrix.

jephianlin

2011-06-27 00:00

Exercise 2.2.12

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