Let u and v be nonzero vectors in R". In Section 5.3 we defined the angle between u and

Chapter 6, Problem 18

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Let u and v be nonzero vectors in R". In Section 5.3 we defined the angle between u and v \0 be the angle () such that (u . v) cosO = - -- Ilu ll llvll A linear operator L: N" -+ R' is called angle prcscn 'ing If the angle between u and v IS the same as that between L(u) and L(v). Prove that if L is inner product preserving (see Exercise 16). then it is angle preserving.

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