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The Generalized Rayleigh Quotient

Published online by Cambridge University Press:  20 November 2018

M. V. Pattabhiraman
M. V. Pattabhiraman*
Affiliation:
University of Calgary, Alberta, Canada
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In this paper we generalize the concept of the Rayleigh quotient to a complex Banach space. Lord Rayleigh investigated the quotient

(1)

considered as a function of the components of q, in the case of a symmetric matrix pencil Aλ+C with A positive definite. It is known that R(q) has a stationary value when q is a characteristic vector of Aλ+C and that

(2)

where qi is a characteristic vector corresponding to the characteristic value λi

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 17 , Issue 2 , 01 June 1974 , pp. 251 - 256
Copyright
Copyright © Canadian Mathematical Society 1974

References

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