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Generalized variance
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<p>The generalized variance is a scalar value which generalizes <a href="/facts/Variance/ULBJKXD1">variance</a> for <a href="/facts/Multivariate_random_variable/qMfooyVf">multivariate random variables</a>. It was introduced by <a href="/facts/Samuel_S._Wilks/SIH0MW7a">Samuel S. Wilks</a>. </p><p>The generalized variance is defined as the <a href="/facts/Determinant/eGYqJ2TF">determinant</a> of the <a href="/facts/Covariance_matrix/kLhgjHC6">covariance matrix</a>, det ( Σ ) {\displaystyle \det(\Sigma )} . It can be shown to be related to the multidimensional scatter of points around their mean. </p><p>Minimizing the generalized variance gives the <a href="/facts/Kalman_filter/wNK7rnbk">Kalman filter</a> gain. </p>