Hi I have the following problem. Let the symmetric matrix M of the form: \begin{bmatrix} A & B \newline B^T & C \newline \end{bmatrix}

We have that $C$ is positive semidefinite. Is there a way to transform the constraint $A-BC^{-1}B^T \leq 0$ to a constraint using matrix $M$?

I know that in case the constraint was $A-BC^{-1}B^T \geq 0$ the answer is $M \geq 0$. But can we say something similar for the negative definite constraint? (I have already checked that $A-BC^{-1}B^T \leq 0 \Leftrightarrow M \leq 0$ Does not hold.) Is there another way to transform this constraint to a linear over the matrix B?

Thank you very much!