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Orthogonal matrices are compact

  1. Apr 28, 2005 #1
    How can you prove that the set of orthogonal matrices are compact? I know why they are bounded but do not know why they are closed.
  2. jcsd
  3. Apr 28, 2005 #2


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    What is the topology?

    (By the way- closed and bounded does not necessarily imply compact.)
  4. Apr 28, 2005 #3


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    how about defining them by an equation?

    and of course closed and bounded does imply compact in a euclidean space such as matrix space. as hurkyl knows very well - he is just trying to scare you.

    (in a general metric space you need "complete and totally bounded")
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