On the construction of a class of invariant polynomials in several matrices, extending the zonal polynomials
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The construction of a class of invariant polynomials in several matrices extending the zonal polynomials is discussed. The method adopted generalized the orginal group-theoretic approach of James . A table of three-matrix polynomials up to degree 5 is presented.
AMS 1970 subject classification62E15 62H10
Key words and phrasesInvariant polynomials zonal polynomials group representations multivariate distributions Young tableaux
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- Chikuse, Y. (1979a). Distributions of some matrix variates and latent roots in multivariate Behrens-Fisher discriminant analysis, to appear inAnn. Statist.Google Scholar
- Chikuse, Y. (1979b). Invariant polynomials with three matrix arguments, extending the polynomials with smaller numbers of matrix arguments, unpublished report.Google Scholar
- Chikuse, Y. (1980). Invariant polynomials with real and complex matrix arguments and their applications, unpublished report, University of Pittsburgh.Google Scholar
- Davis, A. W. (1980a). Invariant polynomials with two matrix arguments, extending the zonal polynomials,Multivariate Analysis—V (ed. P. R. Krishnaiah), 287–299.Google Scholar
- Richards, D. St. P. and Gupta, R. D. (1980). Evaluation of cumulative probabilities for Wishart and multivariate beta matrices and their latent roots, unpublished report, University of the West Indies.Google Scholar