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Triangular representations of linear algebras

Published online by Cambridge University Press:  24 October 2008

M. P. Drazin
M. P. Drazin
Affiliation:
Trinity CollegeCambridge
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Extract

It is well known that the elements of any given commutative algebra (and hence of any commutative set) of n × n matrices, over an algebraically closed field K, have a common eigenvector over K; indeed, the elements of such an algebra can be simultaneously reduced to triangular form (by a suitable similarity transformation). McCoy (5) has shown that a triangular reduction is always possible even for matrix algebras satisfying a condition substantially weaker than commutativity. Our aim in this note is to extend these results to more general systems (our arguments being, incidentally, simpler than some used for the matrix case even by writers subsequent to McCoy).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 49 , Issue 4 , October 1953 , pp. 595 - 600
Copyright
Copyright © Cambridge Philosophical Society 1953

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References

REFERENCES

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