How to show the fact that the set of all orthogonal matrices over $\mathbb C$ is compact
By an orthogonal matrix over $\mathbb C$ I mean a matrix $A$ satisfying $AA^T=I$ and here $A^T=(a_{ji})$ where $A=(a_{ij})$
It is not the same as unitary matrix where in unitary matrix we take transpose and then conjugate or vice versa
I know that set of all orthogonal matrices over $\mathbb R$ is compact.
I think the closedness of the set will follow from the same arguements as in the above case. But the boundedness part not sure