Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
linear operator |
| gptkbp:alsoKnownAs |
gptkb:self-adjoint_operator
|
| gptkbp:category |
functional analysis
operator theory |
| gptkbp:definedIn |
complex Hilbert space
|
| https://www.w3.org/2000/01/rdf-schema#label |
Hermitian operator
|
| gptkbp:introduced |
gptkb:David_Hilbert
|
| gptkbp:property |
eigenvectors corresponding to distinct eigenvalues are orthogonal
all eigenvalues are real equal to its own adjoint can be diagonalized by unitary transformation matrix representation is Hermitian matrix spectrum is real |
| gptkbp:relatedTo |
gptkb:unitary_operator
symmetric operator normal operator skew-Hermitian operator |
| gptkbp:symbol |
A = A†
|
| gptkbp:usedFor |
observables in quantum mechanics
|
| gptkbp:usedIn |
quantum mechanics
|
| gptkbp:bfsParent |
gptkb:self-adjoint_operator
|
| gptkbp:bfsLayer |
7
|