Generalizations
If is a vector-valued random variable, with values in, and thought of as a column vector, then the natural generalization of variance is, where and is the transpose of, and so is a row vector. This variance is a positive semi-definite square matrix, commonly referred to as the covariance matrix.
If is a complex-valued random variable, with values in, then its variance is, where is the conjugate transpose of . This variance is also a positive semi-definite square matrix.
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