There are several threads here about covariance matrix and inverse covariance matrix interpretation ([here][1], [here][2] or [here][3]).

However, I was wondering how to interpret the inverse covariance matrix (or precision matrix) as the covariance matrix can be diagonalized (since it's a definite positive matrix). $$ \Sigma = P D P^{-1} $$ ($\Sigma$ being the covariance matrix and $D$ is a diagonal matrix). Then $$ \Sigma^{-1} = P D^{-1} P^{-1} $$

How to interpret this diagonal precision matrix $D^{-1}$ ? I think I don't get exactly the signification of the eigenvectors $P$ .

Thanks for your help. [1]: How to interpret an inverse covariance or precision matrix? [2]: What does the inverse of covariance matrix say about data? (Intuitively) [3]: Decomposition of inverse covariance matrix

There are several threads here about covariance matrix and inverse covariance matrix interpretation ([here][1], [here][2] or [here][3]).

However, I was wondering how to interpret the inverse covariance matrix (or precision matrix) as the covariance matrix can be diagonalized (since it's a definite positive matrix). $$ \Sigma = P D P^{-1} $$ ($\Sigma$ being the covariance matrix and $D$ is a diagonal matrix). Then $$ \Sigma^{-1} = P D^{-1} P^{-1} $$

How to interpret this diagonal precision matrix $D^{-1}$ ? I think I don't get exactly the signification of the eigenvectors $P$ .

Thanks for your help. [1]: How to interpret an inverse covariance or precision matrix? [2]: What does the inverse of covariance matrix say about data? (Intuitively) [3]: Decomposition of inverse covariance matrix