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Exercise 6.11.12

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Let $β$ be an orthonormal basis. Then we have ${[T]}_{β} = - I_{n}$ , where $n$ is the dimension of $V$ . Since $\det (- I_{n}) = {(- 1)}^{n}$ , we know that $T$ could be decomposed into rotations if and only if $n$ is even by the Corollary after Theorem 6.47.

jephianlin

2011-06-27 00:00

Exercise 6.11.12

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