Definition for "Spectral Radius" in the Quantum Dictionary

Natural & Formal Sciences Dictionary

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.

- Natural & Formal Sciences -

Mathematics & Logic Dictionary

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}.

- Pure Mathematics -

Algebra Dictionary

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.