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Matrix Differentiation of S-Functions

Published online by Cambridge University Press:  20 January 2009

H. O. Foulkes
H. O. Foulkes
Affiliation:
University College, Swansea.
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1. It has been shown (1; 2, 136) that if Sr, ar, hr denote respectively the symmetric functions , Σλ1 λ2…λr, and the homogeneous product sum of degree r of the latent roots λ1, λ2, …, λn of the matrix X = [xij] then

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 10 , Issue 1 , January 1953 , pp. 5 - 10
Copyright
Copyright © Edinburgh Mathematical Society 1953

References

REFERENCES

(1)Turnbull, H. W., “On differentiating a matrix,” Proc. Edinburgh Math. Soc. (2), 1 (1927), 111–128.CrossRefGoogle Scholar
(2)Wedderburn, J. H. M., Lectures on matrices (New York, 1934).CrossRefGoogle Scholar
(3)Littlewood, D. E., Group characters and matrix representations of groups (Oxford, 1940).Google Scholar
(4)Turnbull, H. W., “Matrix differentiation of the characteristic function,” Proc. Edinburgh Math. Soc. (2), 2 (1931), 256–264.CrossRefGoogle Scholar
(5)Foulkes, H. O., “Differential operators associated with S-functions,” Journal London Math. Soc., 24 (1949), 136–143.CrossRefGoogle Scholar
(6)Murnaghan, F. D., Theory of group representations (Baltimore, 1938).Google Scholar