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Inverse multi-parameter eigenvalue problems for matrices*

Published online by Cambridge University Press:  14 November 2011

Patrick J. Browne  and
B. D. Sleeman
Patrick J. Browne
Affiliation:
Department of Mathematics and Statistics, The University of Calgary, Calgary, Alberta, Canada T2N 1N4
B. D. Sleeman
Affiliation:
Department of Mathematical Sciences, University of Dundee, Dundee DD1 4HN, Scotland
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Synopsis

We study the possibility of perturbing a matrix A by a diagonal matrix so that an eigenvalue problem with leading matrix A has specifiedeigenvalues when A is replaced by A+D. The particular cases presented are the one-parameter generalized eigenvalue problem (A× = λB μ×, a two-parameter eigenvalue problem (A + λB + μC)× = 0, a linked system ofsuch two-parameter problems and a quadratic eigenvalue problem (A + λB + λ2C)× = 0. The work extends results of Hadeler for the classical problem A× = λ×.

Information

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 100 , Issue 1-2 , 1985 , pp. 29 - 38
Copyright
Copyright © Royal Society of Edinburgh 1985

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References

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