Cross-correlation matrix
The cross-correlation matrix of two random vectors is a matrix containing as elements the cross-correlations of all pairs of elements of the random vectors.The cross-correlation matrix is used in various digital signal processing algorithms.For two random vectors, each containing random elements whose expected value and variance exist, the cross-correlation matrix ofand has dimensionsWritten component-wise: The random vectorsneed not have the same dimension, and either might be a scalar value.are random vectors, thenmatrix whoseare complex random vectors, each containing random variables whose expected value and variance exist, the cross-correlation matrix ofdenotes Hermitian transposition.Two random vectorsare called uncorrelated if They are uncorrelated if and only if their cross-covariance matrixmatrix is zero.In the case of two complex random vectorsthey are called uncorrelated if and The cross-correlation is related to the cross-covariance matrix as follows: