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So, I saw a few different definitions of the term "Isometry" when I was searching for help on my most recent problem. Not finding anything online here or elsewhere, I went ahead and posted a question here. So I used , then I noticed there was an tag with no description...

Can someone with more knowledge than I add a description? I would, but I'm just starting functional analysis and am not 100% sure on whether it requires $\Vert Tx\Vert=\Vert x\Vert$ or like in my case that $\Vert T(x)-T(y)\Vert=\Vert x-y\Vert$ (The distinction necessary when T is not linear)

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  • $\begingroup$ A fairly general definition of isometry is a map from one metric space to another that preserves distances. So on a normed space it would mean $\|T(x)-T(y)\|=\|x-y\|$, which for a linear map is equivalent to preserving the norm. Then there are local isometries on Riemannian manifolds, which perhaps should be included. $\endgroup$ – Jonas Meyer Jan 29 '15 at 3:47
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    $\begingroup$ How about we just nuke the tag instead of trying to define it? $\endgroup$ – user147263 Jan 29 '15 at 3:57
  • $\begingroup$ @Fundamental I think this is the best course of action. There's no sense in making tags for specific kinds of operators. $\endgroup$ – Cameron Williams Jan 30 '15 at 0:34
  • $\begingroup$ Nuking is fine with me too, just didn't seem right to have an undefined tag. $\endgroup$ – Alan Jan 30 '15 at 0:36

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