For example, if and are random vectors, then
is a matrix whose -th entry is .
For the cross-covariance matrix, the following basic properties apply:[2]
- If and are independent (or somewhat less restrictedly, if every random variable in is uncorrelated with every random variable in ), then
where , and are random vectors, is a random vector, is a vector, is a vector, and are matrices of constants, and is a matrix of zeroes.
Gubner, John A. (2006). Probability and Random Processes for Electrical and Computer Engineers. Cambridge University Press. ISBN 978-0-521-86470-1.