Properties (27)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:theorem
|
| gptkbp:appliesTo |
complex numbers
real numbers inner product spaces |
| gptkbp:canBe |
algebraic manipulation
geometric interpretation vector norms |
| gptkbp:hasRelatedPatent |
machine learning
signal processing quantum_mechanics |
| https://www.w3.org/2000/01/rdf-schema#label |
Cauchy-Schwarz inequality
|
| gptkbp:isA |
fundamental theorem in mathematics
|
| gptkbp:isLocatedIn |
|a1b1 + a2b2 + ... + anbn| ≤ √(a1² + a2² + ... + an²) √(b1² + b2² + ... + bn²)
|
| gptkbp:isRelatedTo |
dot product
norms |
| gptkbp:isUsedIn |
proofs of other inequalities
|
| gptkbp:isUtilizedFor |
optimization problems
functional analysis convex analysis |
| gptkbp:namedAfter |
gptkb:Augustin-Louis_Cauchy
Hermann Schwarz |
| gptkbp:relatedTo |
triangle inequality
|
| gptkbp:specialization |
Cauchy-Schwarz_integral_inequality
|
| gptkbp:state |
|⟨u, v⟩| ≤ ||u|| ||v||
|
| gptkbp:usedIn |
statistics
probability theory linear_algebra |