Spectral radius

The spectral radius of a matrix or a bounded linear operator is the supremum among the moduli of the elements in its spectrum, which is sometimes denoted by ρ(·).

Table of contents

1 Matrix 2 Bounded linear operator 3 External links

Matrix

Let λ₁,...,λ_n be the (real or complex) eigenvalues of a matrix A. Then

ρ(A) := ρ(A) = max(|λ_i|)

The spectral radius of a planar graph is the spectral radius of its adjacency matrix.

For any matrix norm ||·||, we have

ρ(A)=lim_n→∞||Aⁿ||^1/n.

Bounded linear operator

For a bounded linear operator A and the operator norm ||·||, again we have

ρ(A)=lim_n→∞||Aⁿ||^1/n.

External links

• Spectral Radius of Planar Graphs