ThmDex – An index of mathematical definitions, results, and conjectures.
Formulation F11675 on D2011: Euclidean real covariance
F11675
Formulation 0
Let $X, Y \in \text{Random}(\mathbb{R}^{N \times 1})$ each be a D5210: Random real column matrix such that
(i) \begin{equation} \mathbb{E} |X|^2, \mathbb{E} |Y|^2 < \infty \end{equation}
The covariance of $(X, Y)$ is the D4571: Real matrix \begin{equation} \mathbb{E} \left[ (X - \mathbb{E} X) (Y - \mathbb{E} Y)^T \right] \end{equation}