Generalized dispersion matrices for covariance structural analysis (Q908995)

In several situations of covariance structural analysis e.g., variance components estimation or experimental design the population dispersion matrix V is assumed to have the following pattern \(V=\sum^{c}_{i=1}\theta_ iK_ i,\) where V is a linear combination of c matrices \(K_ 1,K_ 2,...,K_ c\) that are independent. Under the assumption that the \(K_ i\)-matrices are simultaneously diagonalizable, methods are developed for deriving eigenvalues of V and also \(V^{-1}\) under some additional assumptions. Illustrative applications in covariance structural analysis are also discussed.