2
$\begingroup$

How do I prove that a map preserves the angle if and only if it's the scalar multiple of an isometry.

I get the "if" direction by using definition of isometry.

How do I show the other direction, i.e. that $$\frac{<u, v>}{\left\lVert u\right\rVert\left\lVert v\right\rVert} = \frac{<L(u), L(v)>}{\left\lVert L(u)\right\rVert\left\lVert L(v)\right\rVert}$$ implies scalar multiple of isometry?

$\endgroup$

Your Answer

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Browse other questions tagged or ask your own question.