# If an inverse covariance matrix is sparse, what can I say about the covariance matrix?

How does the sparsity condition on an inverse covariance matrix affect the actual covariance matrix?

• Unfortunately, it does not Apr 12, 2016 at 13:02
• There's got to be something. For instance identity matrix is sparse, and its inverse too. Jun 23, 2016 at 18:17

$\left[\begin{array}{cc} A & B \\C & D \end{array}\right]^{-1} =\begin{bmatrix} (A - BD^{-1}C)^{-1} & -A^{-1}B(D - CA^{-1}B)^{-1} \\ -D^{-1}C(A - BD^{-1}C)^{-1} & (D - CA^{-1}B)^{-1} \end{bmatrix}$