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Fixed types and TeX
Johannes Hahn
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Why is $O(n;k)$ not connected, and has four connected components?

Why is $O(n;k)$ not connected and has four connected components? $O(n;k) =\{A\in GL(n+k,\mathbb{C}) \mid A^{T}GA=G\}$

where $G=\begin{pmatrix} 1&&&&&\\ &\ddots& & & &\\ &&1&& &\\ && &-1& &\\ && & &\ddots &\\ && & & &-1 \end{pmatrix}$,

and it has n number 1, and k -1