Wp/shi/Targadda n Cauchy–Schwarz

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Ɣ tusnakt, Targadda nɣ tamyagart n Kuci–Scwarz (s tanglizt : Cauchy–Schwarz), tettawsan ula s yism n targadda n Cauchy–Bunyakovsky–Schwarz, tga yat targadda bahra istawhman ɣ tusnakt kullut, ar sis nswurri ɣ aljibr imzirg, taslṭ, tiẓri n tsqqart d kigan n igran yaḍni. Targadda ad issufɣt-id yan umusnak afransis iga s yism Augustin-Louis Cauchy ɣ usggwas n 1821, sliɣ yufa Viktor Bunyakovsky yat targadda trwast akk ɣ mad izdin d aɣrd ɣ usggwas n 1859, mn bɛd yufatt daɣ yan umusnak almani Hermann Amandus Schwarz ɣ usggwas n 1888[1].

Mad tettini

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 ilawn d ismlaln. S ɣmkad, iɣ nusi aẓur uzmir-sin ɣ tsgiwin s snat, d iɣ asn nga alugn. Ar nttafa targadda ad [2][3]:

D yat tɣawsa yaḍn, tasgiwin s snat gaddan iɣ d gan ilelliyn imzirgn (yaɛni gan imsadaɣn).[4][5]

d d ufaris agnsan iga afaris agnsan asmlal anaway, hann targadda tzḍar ad ttyura zund ɣikad (maɣ tirra n taɛṛṛaḍt ar sis nmmal unaftay n ismlaln): i , darnɣ

Ad t igan,

Amawal

  • 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

  1. ( en ) Steele, J. Michael (2004)The Cauchy–Schwarz Master Class: an Introduction to the Art of Mathematical Inequalities
  2. ( 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.
  3. ( en ) Hunter, John K.; Nachtergaele, Bruno (2001). Applied Analysis. World Scientific. ISBN 981-02-4191-7.
  4. ( en ) Bachmann, George; Narici, Lawrence; Beckenstein, Edward (2012-12-06). Fourier and Wavelet Analysis. Springer Science & Business Media. p. 14. ISBN 9781461205050.
  5. ( 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.