| Abstract: | Chikuse's (1987) algorithm constructs top-order invariant polynomials with multiple matrix arguments. Underlying it is a set of simultaneous equations for which all integer solutions must be found. Each solution represents a component of the sum of terms which comprise the polynomial. The system of equations has a specialised structure which may be exploited to obtain a polynomial with r matrix arguments in terms of a polynomial with r-1 matrix arguments. This is demonstrated for two particular polynomials that have two matrix arguments. These results are applied to problems involving expectations of ratios of quadratic forme in normal variables; analytic as well as computable formulae are derived. |
