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Spectral Radius


Let A be an n×n matrix with complex or real elements with eigenvalues lambda_1, ..., lambda_n. Then the spectral radius rho(A) of A is

 rho(A)=max_(1<=i<=n)|lambda_i|,

i.e., the largest absolute value (or complex modulus) of its eigenvalues.

The spectral radius of a finite graph is defined as the largest absolute value of its graph spectrum, i.e., the largest absolute value of the graph eigenvalues (eigenvalues of the adjacency matrix) .


See also

Adjacency Matrix, Algebraic Connectivity, Eigenvalue, Graph Eigenvalue, Graph Spectrum, Laplacian Spectral Radius

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References

Gradshteyn, I. S. and Ryzhik, I. M. Tables of Integrals, Series, and Products, 6th ed. San Diego, CA: Academic Press, pp. 1115-1116, 2000.

Referenced on Wolfram|Alpha

Spectral Radius

Cite this as:

Weisstein, Eric W. "Spectral Radius." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SpectralRadius.html

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