The cross-covariance matrix between two random vectors is a matrix containing the covariances between all possible couples of random variables formed by taking one random variable from one of the two vectors, and one random variable from the other vector.

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This is a formal definition.

Definition Let be a random vector and be a random vector. The cross-covariance matrix between and is a matrix, denoted by and defined as follows:

Define two random vectors and as follows:The cross-covariance matrix between and is

More details about the cross-covariance matrix can be found in the lecture entitled Covariance matrix.

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