3
$\begingroup$

It is well-known that any real anti-symmetric $n \times n$ matrix $A$ can be transformed via
$A \to O A O^T$ into block-diagonal form consisting of $2 \times 2$ antisymmetric matrices, where $O \in SO(n)$ is orthogonal.

It seems that the analogous statement should also hold for $O \in SO(p,n-p)$, or at least for $SO(1,n-1)$. What is the precise statement, and where can one find it?

Improve this question
$\endgroup$
2
  • $\begingroup$ What do you mean by "analogous statement"? I mean, do you take $O\in SO(p,n-p)$ and $A$ in the Lie algebra $\mathfrak so(p,n-p)$? $\endgroup$
    – Claudio Gorodski
    Commented Apr 2, 2012 at 0:58
  • $\begingroup$ 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. $\endgroup$
    – Harold Steinacker
    Commented Apr 3, 2012 at 15:00

0

Reset to default

You must log in to answer this question.

Browse other questions tagged .