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Invariant matrices and S-functions

Published online by Cambridge University Press:  20 January 2009

M. Zia-ud-Din
M. Zia-ud-Din
Affiliation:
University CollegeSwansea.
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It is known that an induced matrix of an induced matrix is expressible as the direct sum of invariant matrices, or more generally that an invariant matrix of an invariant matrix can be expressed as a direct sum of invariant matrices. The spurs of the irreducible invariant matrices of a given matrix A = [ast], are the S-iunctions of the latent roots of A.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 5 , Issue 1 , October 1936 , pp. 43 - 45
Copyright
Copyright © Edinburgh Mathematical Society 1936

References

page 43 note 1 Schur, , “Ueber eine Klasse von Matrizen,” Diss. Berlin (1901).Google Scholar

page 43 note 2 See Littlewood, D.E. and Richardson, , Phil. Trans. Roy. Soc. (A) 233 (1934), 107–115 for definition, and also Schur, loc. cit.CrossRefGoogle Scholar

page 43 note 3 Littlewood, D.E., Journal London Math. Soc. 11 (1936), 49–54. I am indebtedto Mr Littlewood for suggesting the problem.CrossRefGoogle Scholar

page 44 note 1 Schur, , op. cit., pp. 10, 11.Google Scholar

page 44 note 2 Littlewood, D. E. and Richardson, A. R., op. cit., p. 109.Google Scholar

page 44 note 3 Littlewood, and Richardson, , Phil. Trans. Roy. Soc. (A) 233 (1934), 109.CrossRefGoogle Scholar

page 45 note 1 Tables as far as 10th degree will be found in Littlewood's, D. E. paper, Proc. London Math. Soc. (2) 39 (1935), 177–183. The 12th degree table is to appear in Proc. London Math. Soc.Google Scholar