I'm looking for ways to solve the inverse of a symmetric matrix with 1's on the diagonal and all entries $x_{ij}$ continues variables within the range $(-1,1)$. The matrix thus looks like: \begin{bmatrix} 1 & x_{12} & x_{13} & \dots & x_{1m} \\ x_{12} & 1 & x_{23} & \dots & x_{2m} \\ \vdots & \vdots & \vdots & \ddots & \vdots \\ x_{1m} & x_{2m} & x_{3m} & \dots & 1 \end{bmatrix}
Is there a way to solve this matrix analytically for any $m$? How should I go about to try and solve this?
Thanks a lot for any advice on this!
Greets