Index: The Book of Statistical ProofsGeneral Theorems ▷ Probability theory ▷ Covariance ▷ Precision matrix

Definition: Let $X = [X_1, \ldots, X_n]^\mathrm{T}$ be a random vector. Then, the precision matrix of $X$ is defined as the inverse of the covariance matrix of $X$:

$\label{eq:corrmat} \Lambda_{XX} = \Sigma_{XX}^{-1} = \begin{bmatrix} \mathrm{Cov}(X_1,X_1) & \ldots & \mathrm{Cov}(X_1,X_n) \\ \vdots & \ddots & \vdots \\ \mathrm{Cov}(X_n,X_1) & \ldots & \mathrm{Cov}(X_n,X_n) \end{bmatrix}^{-1} \; .$

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Metadata: ID: D74 | shortcut: precmat | author: JoramSoch | date: 2020-06-06, 05:08.