##  [Spectral Radius](/spectral-radius) 

  ##  [Spectral Radius](https://natural.quantumdictionary.io/spectral-radius-0) 

  

 [![Natural & Formal Sciences Dictionary](/sites/default/files/styles/large/public/2026-01/Natural%20%26%20Formal%20Sciences.png.webp?itok=2kCDRVQv)](/topic-specific-dictionaries/natural-formal-sciences)



**Natural & Formal Sciences Dictionary**

 







 

 

 

 



 

 

 

 

Definition

For a bounded linear operator A on a Banach space (or a square matrix), the spectral radius is the nonnegative number given by limsup as n→∞ of ||A^n||^{1/n}; it measures the asymptotic exponential growth rate of iterates of A.

 

 

 

 

 





 

 



 ##  [Spectral Radius](https://mathlogic.quantumdictionary.io/spectral-radius-1) 

  

 [![Mathematics & Logic Dictionary](/sites/default/files/styles/large/public/2026-01/Mathematics%20%26%20Logic.png.webp?itok=UhtTRPnp)](/topic-specific-dictionaries/natural-formal-sciences/mathematics-logic)

- Natural & Formal Sciences -

**Mathematics & Logic Dictionary**

 







 

 

 

 



 

 

 

 

Definition

For a square matrix or a bounded linear operator A on a Banach space, the spectral radius ρ(A) is the supremum of the absolute values of points in the spectrum of A; for matrices it equals max{|λ|: λ eigenvalue of A}.

 

 

 

 

 





 

 



 ##  [Spectral Radius](https://algebra.quantumdictionary.io/spectral-radius-2) 

  

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- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The spectral radius of an operator or matrix is the supremum of the absolute values (moduli) of elements in its spectrum; symbolically r(A)=max{|λ|: λ∈σ(A)} when the maximum exists.