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If I have a real 3x3, symmetric and positive-definite matrix $D$ (the hessian of a convex function) and $J=\left[\array{0 & -1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 0 }\right]$. What properties (if any) will $JD$ have?

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    "Of course $JD$ is going to be anti-symmetric." Are you sure about that? Let $D = \begin{bmatrix}a & b & c \\ b & d & e \\ c & e & f\end{bmatrix}$, for example...2012-07-18
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    thanks, you are right. corrected.2012-07-18

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