Cauchy–Bunyakovsky–Schwarz inequality
GPTKB entity
Statements (26)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:inequality
|
| gptkbp:alsoKnownAs |
gptkb:Cauchy–Schwarz_inequality
gptkb:Schwarz_inequality |
| gptkbp:appliesTo |
inner product
vectors |
| gptkbp:category |
inequalities
|
| gptkbp:field |
gptkb:mathematics
gptkb:inner_product_spaces functional analysis linear algebra |
| gptkbp:firstPublished |
1859
|
| gptkbp:generalizes |
gptkb:Hölder's_inequality
gptkb:Minkowski_inequality gptkb:arithmetic_mean-geometric_mean_inequality |
| https://www.w3.org/2000/01/rdf-schema#label |
Cauchy–Bunyakovsky–Schwarz inequality
|
| gptkbp:namedAfter |
gptkb:Augustin-Louis_Cauchy
gptkb:Hermann_Schwarz gptkb:Viktor_Bunyakovsky |
| gptkbp:sentence |
For all vectors u and v in an inner product space, |⟨u,v⟩| ≤ ||u||·||v||.
|
| gptkbp:usedIn |
gptkb:probability_theory
analysis quantum mechanics statistics proofs of triangle inequality |
| gptkbp:bfsParent |
gptkb:Cauchy–Schwarz_inequality
|
| gptkbp:bfsLayer |
6
|