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Apr 3, 2012 at 15:00 comment added Harold Steinacker I mean $O \in SO(p,n-p)$ and $A$ a real anti-symmetric matrix. Then $O A O^T$ is also anti-symmetric, and there should be a normal form, presumably in terms of block-diagonal matrix consisting of $2 \times 2$ antisymmetric matrices.
Apr 2, 2012 at 0:58 comment added Claudio Gorodski What do you mean by "analogous statement"? I mean, do you take $O\in SO(p,n-p)$ and $A$ in the Lie algebra $\mathfrak so(p,n-p)$?
Apr 1, 2012 at 20:31 history asked Harold Steinacker CC BY-SA 3.0