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:

1964-09-01

Pagination or Media Count:

1.0

Abstract:

A lemma was proved to show that the moments of the s-ith elementary symmetric function esf in s non-null 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 s-1th 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 s-1th esf in the s characteristic roots, theta sub i lambda sub i1 lambda sub i, are derivable from those of the first esf in the lambdas. Upper percentage points 5 and 1 were obtained for the distribution of the s-1th esf in the lambdas 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

Subject Categories:

Distribution Statement:

APPROVED FOR PUBLIC RELEASE