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(·).
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2 Bounded linear operator 3 External links |
Matrix
Let λ1,...,λn be the (real or complex) eigenvalues of a matrix A. Then
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.