##  [Rayleigh's Principle](/rayleighs-principle) 

  ##  [Rayleigh's Principle](https://engineering.quantumdictionary.io/rayleighs-principle-0) 

  

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**Engineering & Applied Technologies Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A variational estimate for the fundamental eigenvalue of a symmetric positive‑definite generalized eigenproblem K φ = λ M φ (e.g., structural vibration), expressed by the Rayleigh quotient R(u) = (uᵀ K u)/(uᵀ M u); the minimum of R over admissible, nonzero trial vectors u equals the smallest eigenvalue, and any admissible trial produces an estimate that is greater than or equal to that true fundam