Moore–Penrose inverse (precursor ideas)
E895655
The Moore–Penrose inverse (precursor ideas) refers to E. H. Moore’s early foundational work on generalized matrix inverses, which laid the groundwork for the modern concept of the Moore–Penrose pseudoinverse.
Statements (45)
| Predicate | Object |
|---|---|
| instanceOf |
historical development of mathematics
ⓘ
mathematical concept ⓘ precursor theory ⓘ |
| associatedWith |
least-squares minimization
ⓘ
projection onto column space ⓘ projection onto row space ⓘ |
| basedOn |
linear transformations between inner product spaces
ⓘ
systems of linear equations ⓘ |
| concerns |
generalized inverses in Hilbert spaces
ⓘ
solutions of overdetermined systems ⓘ solutions of underdetermined systems ⓘ |
| emphasizes |
orthogonality conditions for residuals
ⓘ
uniqueness of generalized solutions ⓘ |
| field |
functional analysis
ⓘ
linear algebra ⓘ matrix theory ⓘ |
| goal |
characterize least-squares solutions uniquely
ⓘ
define generalized inverse for singular matrices ⓘ extend matrix inversion to non-square matrices ⓘ |
| hasApplication |
linear regression
ⓘ
numerical linear algebra ⓘ signal processing ⓘ statistics ⓘ |
| hasConcept |
generalized solution of linear equations
ⓘ
least-squares solution ⓘ minimum-norm solution ⓘ normal equations ⓘ orthogonal projection ⓘ |
| hasMainContributor | E. H. Moore NERFINISHED ⓘ |
| hasMathematicalNature |
algebraic
ⓘ
operator-theoretic ⓘ |
| historicalContext | precursor to Penrose’s 1955 axiomatic characterization of the pseudoinverse ⓘ |
| influenced |
R. Penrose
NERFINISHED
ⓘ
development of generalized inverses ⓘ |
| inspired | Moore–Penrose pseudoinverse NERFINISHED ⓘ |
| isPartOf | history of generalized inverses ⓘ |
| isPrecursorOf | axiomatic characterization of pseudoinverse ⓘ |
| precedes | modern theory of Moore–Penrose inverse ⓘ |
| relatedTo |
Moore–Penrose inverse
NERFINISHED
ⓘ
generalized inverse of a matrix ⓘ pseudoinverse ⓘ |
| timePeriod | early 20th century ⓘ |
| usesConcept |
adjoint operator
ⓘ
null space of a linear operator ⓘ range of a linear operator ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.