Statements (25)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:alsoKnownAs |
gptkb:Hermitian_operator
|
| gptkbp:application |
operator theory
partial differential equations quantum mechanics spectral theory |
| gptkbp:characterizedBy |
⟨Ax, y⟩ = ⟨x, Ay⟩ for all x, y in Hilbert space
|
| gptkbp:definedIn |
gptkb:Hilbert_space
|
| gptkbp:example |
gptkb:momentum_operator_(in_quantum_mechanics)
gptkb:position_operator_(in_quantum_mechanics) Laplacian operator identity operator |
| gptkbp:field |
gptkb:mathematics
functional analysis linear algebra |
| gptkbp:generalizes |
real symmetric matrix
|
| https://www.w3.org/2000/01/rdf-schema#label |
self-adjoint operator
|
| gptkbp:property |
eigenvectors corresponding to distinct eigenvalues are orthogonal
all eigenvalues are real equal to its own adjoint |
| gptkbp:relatedTo |
symmetric operator
|
| gptkbp:bfsParent |
gptkb:Hilbert_spaces
gptkb:unitary_operator gptkb:odd_Fredholm_module |
| gptkbp:bfsLayer |
6
|