Geodesic
The Generalized Rayleigh Quotient
Canadian mathematical bulletin, Tome 17 (1974) no. 2, pp. 251-256

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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 q i is a characteristic vector corresponding to the characteristic value λ i 
Pattabhiraman, M. V. The Generalized Rayleigh Quotient. Canadian mathematical bulletin, Tome 17 (1974) no. 2, pp. 251-256. doi: 10.4153/CMB-1974-049-4
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