Definition:Cross-Covariance Matrix

Definition
Let $\mathbf X = \left({X_1, X_2, \ldots, X_n}\right)^T$ and $\mathbf Y = \left({Y_1, Y_2, \ldots, Y_m}\right)^T$ be random vectors.

Then the cross-covariance matrix of $\mathbf X$ and $\mathbf Y$ is defined by:


 * $\operatorname{cov} \left({\mathbf X, \mathbf Y}\right) = \mathbb E \left[{\left({\mathbf X - \mathbb E \left[{\mathbf X}\right]}\right) \left({\mathbf Y - \mathbb E \left[{\mathbf Y}\right]}\right)^T}\right]$

where this expectation exists.