Solution

Past exam of the mathematics course of the University of Cambridge / 2018 / ia / Paper 1 / 7B / c / Solution

{title2=$\dfrac{x^TAx}{x^TBx}$}

For symmetric $A$ and positive-definite $B$, the generalized Rayleigh quotient is $x^TAx/(x^TBx)$. Its stationary values are the <generalized eigenvalue problem>[generalized eigenvalues] of $Av=\lambda Bv$, and its maximum is the largest such eigenvalue.

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 Incoming links: Generalized Rayleigh quotient