
Accession Number : AD0607099
Title : ON ELEMENTARY SYMMETRIC FUNCTIONS OF THE ROOTS OF TWO MATRICES IN MULTIVARIATE ANALYSIS.
Descriptive Note : Mimeograph series no. 23,
Corporate Author : PURDUE UNIV LAFAYETTE IND
Personal Author(s) : Pillai,K. C. Sreedharan
Report Date : SEP 1964
Pagination or Media Count : 1
Abstract : A lemma was proved to show that the moments of the (si)th elementary symmetric function (esf) in s nonnull characteristic roots, lambda sub i (i = 1, 2, ..., s), of a matrix in multivariate analysis could be derived from those of the ith esf. Using this lemma the first four moments of the (s1)th esf were obtained from those of the first esf already known (Pillai, 1954, 1960; Pillai and Samson, 1959). Further, a second lemma was given showing that the moments of the (s1)th esf in the s characteristic roots, theta sub i = lambda sub i/(1 + lambda sub i), are derivable from those of the first esf in the lambda's. Upper percentage points (5% and 1%) were obtained for the distribution of the (s1)th esf in the lambda's for s = 3 using the moment quotients. An example was given to illustrate the use of this criterion. (Author)
Descriptors : (*STATISTICAL ANALYSIS, MATRICES(MATHEMATICS)), (*STATISTICAL FUNCTIONS, MATRICES(MATHEMATICS)), DISTRIBUTION THEORY, COMPLEX NUMBERS, POLYNOMIALS, ALGEBRA, INTEGRALS, NUMERICAL ANALYSIS
Distribution Statement : APPROVED FOR PUBLIC RELEASE