KnowraSpectral radiusLinked fromLinked fromThe 7 pages that link to Spectral radius, each with the reason it gives.All 7Related 5Compared with 2EigenvalueCompared with: It compresses the full eigenvalue set into one measure of dominant magnitude.Lyapunov exponentCompared with: It captures growth for repeated application of one matrix, not generally a changing sequence.Gauss–Seidel methodRelated: The iteration matrix’s spectral radius determines whether errors shrink asymptotically.Perron–Frobenius theoremRelated: The theorem identifies a positive eigenvalue whose value is exactly this maximum.Gershgorin circle theoremRelated: The farthest disk boundary from the origin gives an immediate upper bound on this quantity.Successive over-relaxationRelated: Convergence of the SOR error iteration requires its iteration matrix to have spectral radius below one.Gelfand–Mazur theoremRelated: The theorem’s conclusion makes each element’s spectrum a singleton.