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I have a nonlinear matrix inequality problem where $A,B,C$ and $M$ are known and $T$ is unknown and I would like to find $T$ that satisfies

$$\begin{bmatrix} T^T M T + A & B \\ B^T & C\end{bmatrix} > 0$$

I am aware that if I had

$$\begin{bmatrix} T^T M T + A & B \\ B^T & C\end{bmatrix} < 0$$

I could use the Schur complement and solve this very easily but I don't :)

Does anyone know of any type of transformation or operation that could be used in my case where I want to find $T$ satisfying

$$\begin{bmatrix} T^T M T + A & B \\ B^T & C\end{bmatrix} > 0$$

Thank you for any tips!

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