Evaluation of Determinants, Characteristic Equations and their Roots for a Class of Patterned Matrices

The variance-covariance matrices arising in the analysis of variance, response-surface fitting and order statistics have special patterns expediting and facilitating their algebraic manipulation. By appropriate triangulation and partitioning devices, the determinants of these matrices can be evaluated from general formulae. The characteristic equations, and sometimes their roots, can also be obtained in a direct single step.