Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-05T09:54:19.190Z Has data issue: false hasContentIssue false

The canonical form of invariant matrices

Published online by Cambridge University Press:  24 October 2008

D. B. Hunter
Affiliation:
Department of Mathematics, University of Bradford, Yorkshire

Extract

1. Introduction. Let A[λ] be the irreducible invariant matrix of a general matrix of order n × n, corresponding to a partition (λ) = (λ1, λ2, …, λr) of some integer m. The problem to be discussed here is that of determining the canonical form of A[λ] when that of A is known.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1970

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Aitken, A. C.The normal form of compound and induced matrices. Proc. London Math. Soc. (2) 38 (1935), 354376.CrossRefGoogle Scholar
(2)Hunter, D. B.On a result in Young's quantitative substitutional analysis. Proc. Edinburgh Math. Soc. (2) 15 (1967), 257262.CrossRefGoogle Scholar
(3)Hunter, D. B.Unitary representations of the unitary group. Proc. Cambridge Philos. Soc. 65 (1969), 377386.CrossRefGoogle Scholar
(4)Littlewood, D. E.On compound and induced matrices. Proc. London Math. Soc. (2) 39 (1935), 370381.Google Scholar
(5)Littlewood, D. E.The theory of group characters, 2nd edition (Oxford, 1950).Google Scholar