---
tag: 06WHP8SE98
kind: concept
name: Rayleigh quotient
msc: [15A18, 15A42]
sources:
  - url: https://en.wikipedia.org/wiki/Rayleigh_quotient
    locator: Bounds for Hermitian M
same_as:
  wikidata: Q1665115
  wikipedia: Rayleigh quotient
---

## Summary

The Rayleigh quotient of a Hermitian matrix $A$ and a nonzero vector $x$ is the number $x^* A x / x^* x$.
It lies between the least and the greatest eigenvalue of $A$.