LFor a fixed symmetric matrix AA, the normalized quadratic form

xTAxxTx\frac{x^T A x}{x^T x}

is called a Rayleigh quotient.

Given a positive definite matrix BB of the same size, the quantity

xTAxxTBx\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.