##  [Rayleigh Quotient](/rayleigh-quotient) 

  ##  [Rayleigh Quotient](https://natural.quantumdictionary.io/rayleigh-quotient-0) 

  

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**Natural & Formal Sciences Dictionary**

 







 

 

 

 



 

 

 

 

Definition

For a Hermitian (or symmetric) matrix A and nonzero vector x, the Rayleigh quotient R(x) is (x* A x)/(x* x), a scalar giving the quadratic form value per unit squared norm of x; for complex vectors x* denotes conjugate transpose.