GENERALIZED DISPERSION MATRICES FOR COVARIANCE STRUCTURAL-ANALYSIS

Matrices V that are linear combinations of linearly independent matrices Ki are considered. If the K-matrices are simultaneously diagonalizable, methods are given for deriving eigenroots (eigenvalues) of V and, when the Kis are also a closed set under multiplication, for deriving V-1. Included are such cases as the K-matrices being powers of a matrix, or Kronecker products of powers of matrices. The methods are extensions of those used for dispersion matrices for balanced-data variance-components models. Applications in covariance structural analysis for (real symmetric) structured dispersion matrices and for other situations are discussed. © 1990.