Linear and multilinear algebra; matrix theory Eigenvalues and eigenvectors Concept
Eigenvalue
Summary
An eigenvalue of a linear map from a space to itself is a scalar with a special property. The map sends some nonzero vector to times that vector.
Where this leads
102 pages build on this one.
- Power iteration
- Hopf bifurcation
- Derivation of the conjugate gradient method
- Conjugate residual method
- Weyl's law
- Point spectrum
- Sylvester equation
- Hilbert–Schmidt expansion theorem
- Hypergeometric function of a matrix argument
- Minimal residual method
- Spectral radius
- Wigner semicircle law
- Interlacing of zeros of orthogonal polynomials
- Maass wave form
- Bochner's classification of orthogonal polynomial eigenfunctions
- Lieb–Thirring inequality
- Karhunen–Loève theorem
- Eigenfunction of an integral operator
- Bilinear series of a symmetric kernel
- Perron–Frobenius theorem
- QR algorithm
- Inverse iteration
- Modified Richardson iteration
- Pseudospectrum
- Sturm–Liouville theory
- Lanczos algorithm
- Counterexample to the Markus–Yamabe conjecture
- Cauchy interlacing theorem
- Lax pair
- Spectral theorem for compact self-adjoint operators
- Courant–Fischer characterization of characteristic values
- Generalized minimal residual method
- Multigrid method
- Conjugate gradient method
- Bauer–Fike theorem
- Halmos–von Neumann theorem
- Canonical correlation
- Stiff equation
- Selberg's 1/4 conjecture
- Spectral geometry
- Rayleigh–Ritz method
- Arthur–Selberg trace formula
- Selberg trace formula
- Parry measure
- Eta invariant
- Divide-and-conquer eigenvalue algorithm
- Matrix pencil
- Arnoldi iteration
- Courant–Fischer min-max theorem
- Eigendecomposition
- Marchenko–Pastur law
- Monodromy theorem for singularities
- Fenichel's theorem
- Hilbert–Pólya conjecture
- Brauer character
- Lidskii's trace formula for integral operators
- Pólya's conjecture on Laplacian eigenvalues
- Min-max theorem
- Inoue surface
- Spectrum of the Laplace–Beltrami operator
- Floquet multiplier
- Bogdanov–Takens bifurcation
- Biconjugate gradient method
- Classification of second-order PDEs
- Spectral theory of compact operators
- Linearized stability theorem for maps
- Jacobi eigenvalue algorithm
- Turing pattern
- Biconjugate gradient stabilized method
- Optimal experimental design
- LOBPCG
- Feit–Higman theorem
- Jentzsch's theorem on positive kernels
- Chebyshev iteration
- Mercer's theorem
- Spectral theory of dynamical systems
- Shilnikov theorem
- Lidskii's theorem
- Principal component analysis
- Hurwitz-stable matrix
- Multidimensional scaling
- Weyl's inequality
- Eigenvalue algorithm
- Spectral theory
- Prolate spheroidal wave functions
- Tracy–Widom distribution
- Roe solver
- Complex powers of elliptic operators
- Strict hyperbolicity
- Schur decomposition
- Singular values of a compact operator
- Schmidt's singular value decomposition of a kernel
- Anderson localization
- Hearing the shape of a drum
- Preconditioner
- Fredholm's theorem
- Rayleigh quotient iteration
- Eigenvalue perturbation
- Schur–Horn theorem
- Dirichlet eigenvalue
- Normal form
- Numerical linear algebra
Further reading
- Web https://en.wikipedia.org/wiki/Eigenvalues_and_eigenvectors, General definition
About this page
| Tag | 0BQAA2BK3Q |
|---|---|
| URI | m2://0BQAA2BK3Q |
| Kind | concept |
| Writing | W0 stub |
| MSC | 15A18 |
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What links here
Definitions
Used by
- Power iteration
- Hopf bifurcation
- Weyl's law
- Point spectrum
- Sylvester equation
- Hypergeometric function of a matrix argument
- Minimal residual method
- Spectral radius
- Wigner semicircle law
- Maass wave form
- Bochner's classification of orthogonal polynomial eigenfunctions
- Lieb–Thirring inequality
- Karhunen–Loève theorem
- Eigenfunction of an integral operator
- Perron–Frobenius theorem
- QR algorithm
- Inverse iteration
- Modified Richardson iteration
- Pseudospectrum
- Sturm–Liouville theory
- Lanczos algorithm
- Counterexample to the Markus–Yamabe conjecture
- Cauchy interlacing theorem
- Lax pair
- Spectral theorem for compact self-adjoint operators
- Generalized minimal residual method
- Bauer–Fike theorem
- Halmos–von Neumann theorem
- Canonical correlation
- Stiff equation
- Selberg's 1/4 conjecture
- Rayleigh–Ritz method
- Selberg trace formula
- Eta invariant
- Divide-and-conquer eigenvalue algorithm
- Matrix pencil
- Arnoldi iteration
- Courant–Fischer min-max theorem
- Eigendecomposition
- Marchenko–Pastur law
- Monodromy theorem for singularities
- Fenichel's theorem
- Hilbert–Pólya conjecture
- Brauer character
- Min-max theorem
- Inoue surface
- Spectrum of the Laplace–Beltrami operator
- Floquet multiplier
- Bogdanov–Takens bifurcation
- Classification of second-order PDEs
- Spectral theory of compact operators
- Linearized stability theorem for maps
- Jacobi eigenvalue algorithm
- Turing pattern
- Optimal experimental design
- LOBPCG
- Feit–Higman theorem
- Chebyshev iteration
- Spectral theory of dynamical systems
- Shilnikov theorem
- Lidskii's theorem
- Principal component analysis
- Hurwitz-stable matrix
- Multidimensional scaling
- Weyl's inequality
- Eigenvalue algorithm
- Spectral theory
- Prolate spheroidal wave functions
- Tracy–Widom distribution
- Roe solver
- Complex powers of elliptic operators
- Strict hyperbolicity
- Schur decomposition
- Singular values of a compact operator
- Anderson localization
- Hearing the shape of a drum
- Preconditioner
- Rayleigh quotient iteration
- Eigenvalue perturbation
- Schur–Horn theorem
- Dirichlet eigenvalue
- Normal form
- Numerical linear algebra
Results about this
- Wigner semicircle law
- Cauchy interlacing theorem
- Bauer–Fike theorem
- Courant–Fischer min-max theorem
- Marchenko–Pastur law
- Min-max theorem
- Weyl's inequality