# Eigenstructure and condition number of a block symmetric matrix

Consider a block, symmetric matrix $$\begin{pmatrix} 0 & -A^T \\ A & C \end{pmatrix}$$ where $$A$$ and $$C$$ are two real positive definite matrices. What is the condition number of that matrix? Is it related to the condition number of $$A^T C^{-1} A$$?