Let $n$ variates possessing finite first and second moments be partitioned into $k$ sets. A system of equations is developed for which some solution consists of $k$ sets of coefficients which combine the $k$ sets of variates into $k$ variates possessing minimum generalized variance.
"Minimum Generalized Variance for a set of Linear Functions." Ann. Math. Statist. 22 (3) 456 - 460, September, 1951. https://doi.org/10.1214/aoms/1177729594