Distribution of the Sum of Roots of a Determinantal Equation under a Certain Condition

Abstract

This paper is in continuation of the author's first two papers [1] and [2]. In this paper a method is described by which it is possible to derive the distribution of the sum of roots of a certain determinantal equation under the condition that $m = 0$. This condition implies, when the results are applied to canonical correlations, that the numbers of variates in the two sets differ by unity. The distributions for the sum of roots under this condition have been obtained for $l$ = 2, 3 and 4 and are given in this paper. This paper also derives the moments of these distributions.