Generalized variance

The generalized variance is a scalar value which generalizes variance for multivariate random variables. It was introduced by Samuel S. Wilks.

The generalized variance is defined as the determinant of the covariance matrix, ${\displaystyle \det(\Sigma )}$. It can be shown to be related to the multidimensional scatter of points around their mean.¹

Minimizing the generalized variance gives the Kalman filter gain.²