Linear and multilinear algebra; matrix theory Eigenvalues and eigenvectors Concept
Spectral radius
Summary
The spectral radius of a square complex matrix is the largest absolute value of its eigenvalues. It controls the long-run growth of the powers : they tend to exactly when the spectral radius is less than . It is bounded by every operator norm, and Gelfand's formula recovers it from the norms of the powers.
Where this leads
26 pages build on this one.
- Derivation of the conjugate gradient method
- Conjugate residual method
- Minimal residual method
- Gelfand's formula
- Perron–Frobenius theorem
- Successive over-relaxation
- Modified Richardson iteration
- Generalized minimal residual method
- Multigrid method
- Conjugate gradient method
- Jacobi method
- Parry measure
- M-matrix
- Iterative method
- Gauss–Seidel method
- Volterra operator
- Biconjugate gradient method
- Linearized stability theorem for maps
- Spectral radius formula
- Biconjugate gradient stabilized method
- Jentzsch's theorem on positive kernels
- Chebyshev iteration
- Krein–Rutman theorem
- Stein equation
- Matrix function
- Symmetric successive over-relaxation
Further reading
About this page
| Tag | 9V7YQA85PC |
|---|---|
| URI | m2://9V7YQA85PC |
| Kind | concept |
| Writing | W0 stub |
| MSC | 15A18, 15A60 |
| Same as |
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Used by
- Gelfand's formula
- Perron–Frobenius theorem
- Successive over-relaxation
- Modified Richardson iteration
- Jacobi method
- M-matrix
- Iterative method
- Gauss–Seidel method
- Volterra operator
- Linearized stability theorem for maps
- Spectral radius formula
- Jentzsch's theorem on positive kernels
- Krein–Rutman theorem
- Stein equation
- Matrix function
- Symmetric successive over-relaxation