Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:inequality
|
| gptkbp:alternativeName |
gptkb:Cauchy–Bunyakovsky–Schwarz_inequality
gptkb:Cauchy_inequality gptkb:Schwarz_inequality |
| gptkbp:appliesTo |
gptkb:Euclidean_space
gptkb:Hilbert_spaces gptkb:inner_product_spaces |
| gptkbp:field |
mathematical analysis
linear algebra |
| gptkbp:firstPublished |
1821
|
| 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–Schwarz inequality
|
| gptkbp:namedAfter |
gptkb:Augustin-Louis_Cauchy
gptkb:Hermann_Amandus_Schwarz |
| gptkbp:sentence |
For all vectors u and v in an inner product space, |⟨u,v⟩| ≤ ||u||·||v||
|
| gptkbp:usedIn |
gptkb:probability_theory
functional analysis statistics proofs of triangle inequality |
| gptkbp:bfsParent |
gptkb:Augustin-Louis_Cauchy
|
| gptkbp:bfsLayer |
5
|