Operator theory Particular families of operators Concept
Self-adjoint operator
Summary
A self-adjoint operator on a finite-dimensional inner product space is a linear map from the space to itself that equals its adjoint.
Where this leads
18 pages build on this one.
- Feldman–Hájek theorem
- Rayleigh–Ritz method
- Eta invariant
- Stone's theorem on one-parameter unitary groups
- Dirichlet form
- Mathematical formulation of quantum mechanics
- Min-max theorem
- Zeta-regularized determinant
- Strang splitting
- Lie–Trotter product formula
- Monotone operator method for Hammerstein equations
- Friedrichs extension
- LOBPCG
- Frame operator
- Prolate spheroidal wave functions
- Spectral triple
- Complex powers of elliptic operators
- Anderson localization
Further reading
About this page
| Tag | 0NEGN5CRSC |
|---|---|
| URI | m2://0NEGN5CRSC |
| Aliases | hermitian-operator |
| Kind | concept |
| Writing | W1 stated |
| MSC | 47B15, 15B57 |
| Specializes | Normal operator |
| Same as |
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What this page needs for W2
- edge instance_of in: at least two examples (1 of 2)
- edge not_instance_of in: at least one non-example (0 of 1)
The writing levels say how complete the text of a page is. They do not measure its truth.
What links here
Definitions
Used by
- Feldman–Hájek theorem
- Rayleigh–Ritz method
- Eta invariant
- Stone's theorem on one-parameter unitary groups
- Dirichlet form
- Mathematical formulation of quantum mechanics
- Min-max theorem
- Zeta-regularized determinant
- Lie–Trotter product formula
- Monotone operator method for Hammerstein equations
- Friedrichs extension
- Frame operator
- Prolate spheroidal wave functions
- Spectral triple
- Complex powers of elliptic operators
- Anderson localization