Suppose $Z$ is a complex (Wishart) matrix. Let $a=\frac{1}{[Z^{-1}]_{kk}}$, where $Z^{-1}$ is the inverse of $Z$ and $[Z^{-1}]_{kk}$ represents the $(k,k)$-th entry of $Z^{-1}$.
When I was reading an article, I saw that they define $Z_{kk}^{\text{SC}}$ as the Schur complement of $Z_{kk}$, and they claim that $a=\frac{\text{det}Z} {\text{det}Z_{kk}}=\text{det}Z_{kk}^{\text{SC}}$.
Could you please tell me what does the Schur complement mean? and how I can prove the above claim ?