# Can one have a condition like this in semidefinite programming?

Is it possible to have the following condition in a semidefinite programming as a constraint?

$M= \left[ {\begin{array}{cc} a & \sqrt{u} \\ \sqrt{u} & b \\ \end{array} } \right] \geq 0$

where $\geq 0$ means positive semidefinite.

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## migrated from cstheory.stackexchange.comFeb 12 '13 at 23:45

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However, if there are some constraints over $a$, $b$ and $u$ it can be, right? –  Alex Grilo Feb 13 '13 at 19:44