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, . It can be shown to be related to the multidimensional scatter of points around their mean.{{cite book|last1=Kocherlakota|first1=S.|last2=Kocherlakota|first2=K.|chapter=Generalized Variance|url=https://onlinelibrary.wiley.com/doi/10.1002/0471667196.ess0869|title=Encyclopedia of Statistical Sciences|year=2004 |publisher=Wiley Online Library|doi=10.1002/0471667196.ess0869 |isbn=0471667196 |accessdate=30 October 2019}}
Minimizing the generalized variance gives the Kalman filter gain.Proof that the Kalman gain minimizes the generalized variance,
Eviatar Bach https://arxiv.org/abs/2103.07275