In the first problem set of chapter 1, problem 1-8(b) deals with angle preserving transformations. In the newest edition of the book the problem is stated(adsbygoogle = window.adsbygoogle || []).push({});

If there is a basis x_1, x_2, ...., x_n and numbers a_1, a_2, ...., a_n such that Tx_i = a_i x_i, then the transformation T is angle preserving if and only if all |a_i| are equal.

In the first edition (the one with the cool blue diagrams that you can actually see), the absolute value bars are omitted on the a_i. However, I'm pretty sure there are counterexamples to both formulations. If the basis happened to be orthogonal, then equal absolute values of the a_i would be enough, but if the basis were oblique, then you would need equality of the a_i. But the author doesn't mention orthogonality until a couple exercises later. Am I missing something?

thanks.

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# Typo in spivak's calculus on manifolds?

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