Statements (34)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:basisFor |
quantum observables
|
| gptkbp:closure_under |
addition
matrix multiplication (if matrices commute) scalar multiplication (by real numbers) |
| gptkbp:definedIn |
complex numbers
|
| gptkbp:diagonal_elements |
real numbers
|
| gptkbp:dimensions |
n x n (square matrices)
|
| gptkbp:field |
gptkb:mathematics
linear algebra |
| gptkbp:generalizes |
real symmetric matrices
|
| gptkbp:hasSpecialCase |
normal matrices
|
| https://www.w3.org/2000/01/rdf-schema#label |
Hermitian matrices
|
| gptkbp:matrix_element_property |
a_{ij} = conjugate(a_{ji})
|
| gptkbp:namedAfter |
gptkb:Charles_Hermite
|
| gptkbp:property |
eigenvectors corresponding to distinct eigenvalues are orthogonal
all eigenvalues are real equal to its own conjugate transpose |
| gptkbp:relatedTo |
gptkb:spectral_theorem
self-adjoint operators unitary matrices positive definite matrices skew-Hermitian matrices |
| gptkbp:used_in |
gptkb:machine_learning
gptkb:signal_processing engineering functional analysis operator theory physics quantum mechanics statistics |
| gptkbp:bfsParent |
gptkb:Weyl's_theorem
gptkb:spectral_theorem |
| gptkbp:bfsLayer |
5
|