While reading on Gaussian Discriminant Analysis, I came across a derivation of the parameters (specifically, $\sum$) using Maximum Likelihood Estimation that claimed that the MLE of $\sum$ is equivalent to the MLE of $\sum^{-1}$, $\sum$ being the covariance matrix of the multivariate Gaussian distribution.
Though I am able to reach the same result without using the above, I want to know:
- Why does this hold true?
- Does this hold true for any positive definite matrix $A \in \mathbb S_{++}^{n}$, or does the fact that $\sum$ is a covariance matrix play a role in proving this.
