Spectral radius
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In mathematics, 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(·).
Matrix
Let λ1,...,λn be the (real or complex) eigenvalues of a matrix A. Then
- ρ(A) := max(|λi|)
The spectral radius of a planar graph is the spectral radius of its adjacency matrix.
For any matrix norm ||·||, we have
- ρ(A)=limn→∞||An||1/n.
Bounded linear operator
For a bounded linear operator A and the operator norm ||·||, again we have
- ρ(A)=limn→∞||An||1/n.
External links
- Spectral Radius of Planar Graphs (http://www.cs.uwa.edu.au/~gordon/remote/planareig.html)