Let $A:=\{a_{ij}\}$ be an $n\times n$ symmetric, and positive definite matrix. It's well known that, for some $n$-vector $x$, $x'Ax$ is a scalar: $$ x'Ax=\sum_{i=1}^n\sum_{j=1}^n a_{ij}x_i x_j. $$ What can be said about the quadratic form $x'A^{-1}x$?
Is it possible to write is as a function of the $a_{ij}$?