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Improving certain simple eigenvalue bounds

Published online by Cambridge University Press:  24 October 2008

Seppo Hyydö ,
Jorma Kaarlo Merikoski  and
Ari Virtanen
Seppo Hyydö
Affiliation:
University of Tampere, Finland
Jorma Kaarlo Merikoski
Affiliation:
University of Tampere, Finland
Ari Virtanen
Affiliation:
University of Tampere, Finland
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Extract

Throughout this paper we let A = (aij) be a non-zero n × n matrix-we study real matrices only–with row sums R1,…Rn and eigenvalues λ1,…,λn, ordered λ1≥…≥λn if they are real. We denote E = (1,…,1)T and su A = ΣiΣjaij = ETAE. If A is symmetric, a simple property of the Rayleigh quotient is that

satisfies

and

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 99 , Issue 3 , May 1986 , pp. 507 - 518
Copyright
Copyright © Cambridge Philosophical Society 1986

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References

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