The generalized variance is a scalar value which generalizes

variance In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its population mean or sample mean. Variance is a measure of dispersion, meaning it is a measure of how far a set of number ...

for multivariate random variables. It was introduced by Samuel S. Wilks. The generalized variance is defined as the

determinant In mathematics, the determinant is a scalar value that is a function of the entries of a square matrix. It characterizes some properties of the matrix and the linear map represented by the matrix. In particular, the determinant is nonzero if ...

of the covariance matrix,

\det(\Sigma)

. It can be shown to be related to the multidimensional scatter of points around their mean.

References

{{statistics-stub Covariance and correlation