Jordan decomposition theorem
GPTKB entity
Statements (17)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:alsoKnownAs |
gptkb:Jordan–Chevalley_decomposition
|
| gptkbp:appliesTo |
linear operators
square matrices |
| gptkbp:component |
nilpotent part
semisimple part |
| gptkbp:field |
linear algebra
|
| gptkbp:firstDescribed |
19th century
|
| gptkbp:generalizes |
gptkb:diagonalization_theorem
|
| https://www.w3.org/2000/01/rdf-schema#label |
Jordan decomposition theorem
|
| gptkbp:namedAfter |
gptkb:Camille_Jordan
|
| gptkbp:state |
Every square matrix over an algebraically closed field can be decomposed into a sum of a diagonalizable matrix and a nilpotent matrix that commute.
|
| gptkbp:usedIn |
representation theory
matrix theory Lie algebra theory |
| gptkbp:bfsParent |
gptkb:Hahn_decomposition_theorem
|
| gptkbp:bfsLayer |
6
|