Orthogonal matrices are compact

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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.
 

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  • #2
HallsofIvy
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What is the topology?


(By the way- closed and bounded does not necessarily imply compact.)
 
  • #3
mathwonk
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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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