So I am working on a problem and which basically looks like this
$- \frac{x^t A^{-1}x}{M x^TA^{-2}x}$ where $M$ is a scalar, $x$ is a vector and $A$ is a matrix (which in the actual problem is the hessian matrix and so is positive definite).
My question is, can the vector matrix products essentially "cancel" to leave me with just $\frac{1}{MA^{-1}}$?