# A schur complement application

Hi all,

I would like to know if there’s someone can help me with this question:

If the following

\left[ {\begin{array}{*{20}{c}} {{A^T}P + {K^T}{B^T}P + PA + PBK + C_z^T{C_z}}&{P{B_w}} \\ {B_w^TP}&{ - \gamma } \end{array}} \right] \prec 0

is equivalent to (by schur complement)

\left[ {\begin{array}{*{20}{c}} {{A^T}P + {K^T}{B^T}P + PA + PBK}&{C_z^T}&{P{B_w}} \\ {{C_z}}&{ - 1}&0 \\ {B_w^TP}&0&{ - \gamma } \end{array}} \right] \prec 0

Thank you very much in advance.

Kind regards,
Lam

This really isn’t a CVX-specific question. Please post this in a more appropriate forum, like Math StackExchange.