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Exercise 6.11.9

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If $T$ is a rotation, its decomposition contains no reflection. Hence we have $\det (T) = 1$ by Theorem 6.47. If $T$ is a reflection, then we have its decomposition could contain exactly one reflection. Hence we have $\det (T) = - 1$ by Theorem 6.47. So $T$ cannot be both a rotation and a reflection.

jephianlin

2011-06-27 00:00

Exercise 6.11.9

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