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Cross-covariance matrix

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.

Definition

This is a formal definition.

Definition Let X be a Kx1 random vector and Y be a $L\times 1$ random vector. The cross-covariance matrix between X and Y is a $K\times L$ matrix, denoted by [eq1] and defined as follows:[eq2]

Example

Define two random vectors X and Y as follows:[eq3]The cross-covariance matrix between X and Y is[eq4]

More details

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

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