Rayleigh quotient

LFor a fixed symmetric matrix $A$, the normalized quadratic form $$\frac{x^T A x}{x^T x}$$ is called a Rayleigh quotient.

Given a positive definite matrix $B$ of the same size, the quantity $$\frac{x^T A x}{x^T Bx}$$ is called a generalized Rayleigh quotient.

References

1. https://www.sjsu.edu/faculty/guangliang.chen/Math253S20/lec4RayleighQuotient.pdf
2. Gilbert Strang, Linear Algebra and its Applications, ch. 6.4, p. 379, 4th ed., 2006.