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Spectral radius

In mathematics, the spectral radius of a square matrix is the maximum of the absolute values of its eigenvalues. More generally, the spectral radius of a bounded linear operator is the supremum of the absolute values of the elements of its spectrum. The spectral radius is often denoted by ρ ( ⋅ ) {\displaystyle \rho (\cdot )} .

Measurement, Definition & Upper bounds

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Definition

Natural matrix normCharacteristic polynomialHermitian matrixEuclidean normDiagonalizable
13 related topics

Upper bounds

Sub-multiplicative matrix normEigenvectorEigenvalue
3 related topics

Symmetric matrices

SymmetricOrthonormal
2 related topics

Power sequence

Jordan normal form
1 related topics

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Overview

Definition

Upper bounds

Symmetric matrices

Power sequence

Gelfand's formula

Bibliography

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Spectral radius

Nodes36
Edges35
Triples32
Avg. degree1.94
Density0.055556
Components1

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Spectral radius

Top relations

related to Matrices · 6
Spectral radius → Both, Cn, Gelfand's, Indeed, Let, The
related to Power sequence · 5
Spectral radius → Cn, Let, The, Then, Theorem
related to Upper bounds on the spectral radius of a matrix · 5
Spectral radius → Cn, Let, Proposition, The, Then
related to Bounded linear operators · 4
Spectral radius → Banach, In, The, We
related to Graphs · 3
Spectral radius → In, The, This
see also · 3
Spectral radius → Joint, Power, Spectrum
related to Gelfand's formula · 2
Spectral radius → Gelfand's, Israel Gelfand
related to Upper bounds for spectral radius of a graph · 2
Spectral radius → For, There
is a · 1
Spectral radius → generalization of the spectral radius to sets of matrices.Spectrum of a matrixSpectral abscissa
related to Corollary · 1
Spectral radius → Gelfand's

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Important terminology

displaystyle spectral matrix radius rho lambda bounded norm linear cdot values graph matrices gelfand's formula theorem proof eigenvalues since operator

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Spectral radiusis ageneralization of the spectral radius to sets of matrices.Spectrum of a matrixSpectral abscissa0.90text
Spectral radiusrelated to Bounded linear operatorsIn0.60section
Spectral radiusrelated to Bounded linear operatorsBanach0.60section
Spectral radiusrelated to Bounded linear operatorsWe0.60section
Spectral radiusrelated to Bounded linear operatorsThe0.60section
Spectral radiusrelated to CorollaryGelfand's0.60section
Spectral radiusrelated to Gelfand's formulaGelfand's0.60section
Spectral radiusrelated to Gelfand's formulaIsrael Gelfand0.60section
Spectral radiusrelated to GraphsThe0.60section
Spectral radiusrelated to GraphsThis0.60section
Spectral radiusrelated to GraphsIn0.60section
Spectral radiusrelated to MatricesLet0.60section

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