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Is there a norm of the group isometry of a space metric X? EXample X is metric complete of dimimension arbitrary: Merci.

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Peut-etre vous devriez poser votre question en francais? – Pete L. Clark Apr 25 2011 at 8:07
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 Not sure what this means either (though I'm French) - anyway, my 2 cents: any group is the group of isometry of a metric space. So asking a question about isometry groups or just groups is the same (unless the isometric action is involved somehow). Not sure what a "norm" should be here... – Julien Melleray Apr 25 2011 at 9:24
I interpreted it as asking: is there a natural metric one can put on the space of isometries of a metric space? – Todd Trimble Apr 25 2011 at 11:25

closed as not a real question by Yemon Choi, Alain Valette, Bill Johnson, Andreas Thom, Ryan Budney Jan 6 2012 at 0:03

1 Answer

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In matrix analysis, we say that a matrix A preserves the norm||.||, if ||AX||=||X|| for all X. a collection of such matrices makes a group, that is called isometry group for such norm. for example the isometry group for L2-norm contains of all unitary matrices.

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