Are Orthogonal Matrices 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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What is the topology?


(By the way- closed and bounded does not necessarily imply compact.)
 
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")
 
Thread 'Derivation of equations of stress tensor transformation'

Thread 'Derivation of equations of stress tensor transformation'

Hello ! I derived equations of stress tensor 2D transformation. Some details: I have plane ABCD in two cases (see top on the pic) and I know tensor components for case 1 only. Only plane ABCD rotate in two cases (top of the picture) but not coordinate system. Coordinate system rotates only on the bottom of picture. I want to obtain expression that connects tensor for case 1 and tensor for case 2. My attempt: Are these equations correct? Is there more easier expression for stress tensor...
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