Targadda n Kuci–Cwarz
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Ɣ tusnakt, Targadda nɣ tamyagart n Kuci–Scwarz (s tanglizt : Cauchy–Schwarz), ⵜⵜⵡⴰⵢⵙⴰⵏ ula s ⵉⵙⵎ n targadda n Cauchy–Bunyakovsky–Schwarz, tga yat targadda ⵜⴰⴼⵔⴰⵔⵜ ɣ tusnakt ⴰⴽⴽⵯ , ar sis nswurri ɣ ⴰⵍⴳⴰⴱⵔ ⵉⵎⵣⵔⵉⴳ , tiẓri n tsqqart d kigan n igran yaḍni. Targadda ad issufɣt-id yan umusnak afransis iga s yism Augustin-Louis Cauchy ɣ ⵓⵙⴳⴳⵯⴰⵙ ⵏ 1821, sliɣ yufa Viktor Bunyakovsky yat targadda trwast akk ɣ mad izdin d aɣrd ɣ ⵓⵙⴳⴳⵯⴰⵙ n 1859, v tgira yufatt daɣ yan umusnak [ⴳⵓ ⴰⵍⵉⵎⴰⵏ ]] Hermann Amandus Schwarz ɣ ⵓⵙⴳⴳⵯⴰⵙ n 1888[1].
ⵎⴰⴷ ⵜⵉⵏⵉ
[ssnfl | Snfl asagm]Ar ttini targadda n Cauchy–Schwarz mas i akk sin imawayn d n yat tallunt gis afaris agnsan hann rad darnɣ tili
maɣ iga yan ufaris agnsan. S umdya afaris agnsan gis afaris afsnan n utul d arafrar S ɣmka-d, iɣ nusi aẓur uzmir-sin ɣ ⵜⵉⵙⴳⴳⵯⵉⵏ s snat, d iɣ asn nga alugn. Ar nttafa targadda ad [2][3]:
D yat tɣawsa yaḍn, tasgiwin s snat gaddan iɣ d gan ilulliyn imzirgn (ra nini gan imsadaɣn).[4][5]
Iɣ d d ufaris agnsan iga afaris agnsan usniy anaway, hann targadda tZḍaR ad ttyara zund ɣika-d (maɣ tirra n arafrar ar sis nmmal unaftay n ismlaln): i , darnɣ
Ad t igan,
Amawal
[ssnfl | Snfl asagm]- Targadda = inegalite
- Aljibr imzirg = Algebre lineaire
- Taslṭ = analyse
- Tiẓri = theorie
- Tasqqart = probabilite
- Amusnak = mathematicien
- Aɣrd = intagral
- Amaway = vecteur
- Tallunt = espace
- Afaris = produit
- Agnsan = interne
- Afsnan = scalaire
- Ilawn = reel
- Ismlaln = complexe
- Aẓur = racine
- Uzmir-sin = carree
- Alugn = norme
- Tilelli timzirgt = independance lineaire
- Imsadaɣn = paralleles
- Anaway = standard
- Anaftay = conjuge
Isaɣuln
[ssnfl | Snfl asagm]- ↑ ( en ) Steele, J. Michael (2004)The Cauchy–Schwarz Master Class: an Introduction to the Art of Mathematical Inequalities
- ↑ ( en ) Strang, Gilbert (19 July 2005). "3.2". Linear Algebra and its Applications (4th ed.). Stamford, CT: Cengage Learning. pp. 154–155. ISBN 978-0030105678.
- ↑ ( en ) Hunter, John K.; Nachtergaele, Bruno (2001). Applied Analysis. World Scientific. ISBN 981-02-4191-7.
- ↑ ( en ) Bachmann, George; Narici, Lawrence; Beckenstein, Edward (2012-12-06). Fourier and Wavelet Analysis. Springer Science & Business Media. p. 14. ISBN 9781461205050.
- ↑ ( en ) Hassani, Sadri (1999). Mathematical Physics: A Modern Introduction to Its Foundations. Springer. p. 29. ISBN 0-387-98579-4.
Equality holds iff <c|c>=0 or |c>=0. From the definition of |c>, we conclude that |a> and |b> must be proportional.