Show that the set of all orthogonal matrices in the set of all $n \times n$ matrices endowed with any norm topology is compact.
Compactness of the set of $n \times n$ orthogonal matrices
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matrices
compactness
orthogonal-matrices
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2The column vectors of an orthogonal matrix are unit vectors. And there are $n$ column vectors. – 2011-01-23
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0It would also be expeditious to use the operator norm. What is the operator norm of an orthogonal matrix? – 2011-01-23