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XV.—A Matrix Analogue of the Integral

Published online by Cambridge University Press:  14 February 2012

Henry Jack
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Synopsis

A multiple integral, whose integrand is an n × n determinant, is evaluated over certain regions of n-dimensional space. Similar integrals are encountered in the theory of Zonal polynomials. In the course of the work a partition problem arises. In the next paper of these Proceedings, Professor Rutherford enumerates these partitions and relates the subject to the theory of the representation of the symmetric group.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 67 , Issue 3 , 1967 , pp. 205 - 214
Copyright
Copyright © Royal Society of Edinburgh 1967

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References

References to Literature

Aitken, A. C., 1939. Determinants and Matrices. Edinburgh.Google Scholar
Constantine, A. G., 1963. “Some non-central distribution problems in multi-variate analysis,”, Ann. Math. Statist., 34, 1270–1285.Google Scholar
Hua, L. K., 1963. “Harmonic Analysis of functions of several complex variables in the classical domains”, Amer. Math. Soc. Transl., 6.Google Scholar
Herz, C. S., 1955. “Bessel functions of matrix argument”, Ann. Math. Princeton, 61, 474–523.Google Scholar
Jack, H., 1962. “An integral over the interior of a simplex”, Proc. Edin. Math. Soc., 13, 167–171.Google Scholar
Jack, H., 1966. “Jacobians of transformations involving orthogonal matrices”, Proc. Roy. Soc. Edin., A, 67, 81–103.Google Scholar
Jack, H., and Macbeath, A. M., 1959. “The volume of a certain set of matrices”, Proc. Camb. Phil. Soc., 55, 213–223.Google Scholar
James, A. T., 1960. “The distribution of the latent roots of the covariance matrix”, Ann. Math. Statist., 31, 151–158.Google Scholar
James, A. T., 1961. “The distribution of non-central means with known covariance”, Ann. Math. Statist., 32, 874–882.Google Scholar
James, A. T., 1961a. “Zonal polynomials of the real positive definite symmetric matrices”, Ann. Math. Princeton, 74, 456–469.Google Scholar