Ẓṛ asagm n Targadda n Kuci–Cwarz

{{Amgrad icqqan}}

Ɣ [[tusnakt]], Targadda nɣ tamyagart n '''Kuci–Scwarz''' (s [[Tutlayt Tanglizt|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 [[Fransa|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<ref>'''<small>( en )</small>''' Steele, J. Michael (2004)[http://www-stat.wharton.upenn.edu/~steele/Publications/Books/CSMC/CSMC_index.html ''The Cauchy–Schwarz Master Class: an Introduction to the Art of Mathematical Inequalities'']</ref>.

== ⵎⴰⴷ ⵜⵉⵏⵉ  ==
Ar ttini targadda n Cauchy–Schwarz mas i akk sin imawayn <math display="inline">u</math> d <math display="inline">v</math> n yat [[Tallunt ufaris agnsan|tallunt gis afaris agnsan]] hann rad darnɣ tili

<math>|\langle \mathbf{u},\mathbf{v}\rangle| ^2 \leq \langle \mathbf{u},\mathbf{u}\rangle \cdot \langle \mathbf{v},\mathbf{v}\rangle</math>

maɣ <math>\langle\cdot,\cdot\rangle</math> iga yan [[Afaris agnsan|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 <ref name="Strang5">'''<small>( en )</small>''' Strang, Gilbert (19 July 2005). "3.2". ''Linear Algebra and its Applications'' (4th ed.). Stamford, CT: Cengage Learning. pp. 154–155. ISBN <bdi>978-0030105678</bdi>.</ref><ref name=":0">'''<small>( en )</small>''' Hunter, John K.; Nachtergaele, Bruno (2001). ''Applied Analysis''. World Scientific. ISBN <bdi>981-02-4191-7</bdi>.</ref>: 

: <math>|\langle \mathbf{u},\mathbf{v}\rangle| \leq \|\mathbf{u}\|  \|\mathbf{v}\|.</math>

D yat tɣawsa yaḍn, tasgiwin s snat gaddan iɣ <math display="inline">\mathbf{u}</math> d <math display="inline">\mathbf{v}</math> gan ilulliyn imzirgn (ra nini  gan imsadaɣn).<ref>'''<small>( en )</small>''' Bachmann, George; Narici, Lawrence; Beckenstein, Edward (2012-12-06). ''Fourier and Wavelet Analysis''. Springer Science & Business Media. p. 14. ISBN <bdi>9781461205050</bdi>.</ref><ref>'''<small>( en )</small>''' Hassani, Sadri (1999). ''Mathematical Physics: A Modern Introduction to Its Foundations''. Springer. p. 29. ISBN <bdi>0-387-98579-4</bdi>. <q>Equality holds iff <c|c>=0 or |c>=0. From the definition of |c>, we conclude that |a> and |b> must be proportional.</q></ref> 

Iɣ <math display="inline">u_1,\ldots, u_n\in\mathbb C</math> d <math display="inline">v_1,\ldots, v_n\in\mathbb C</math> 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 <math>\mathbf{u},\mathbf{v}\in\mathbb C^n</math>, darnɣ 

<math>\left|\langle \mathbf{u},\mathbf{v} \rangle\right|^2 =\left|\sum_{k=1}^{n}u_k\bar{v}_k\right|^2\leq \langle\mathbf{u},\mathbf{u}\rangle\langle\mathbf{v},\mathbf{v} \rangle = \left(\sum_{k=1}^{n}u_k\bar{u}_k\right)\left(\sum_{k=1}^{n}v_k\bar{v}_k\right) = \sum_{j=1}^n |u_j|^2 \sum_{k=1}^n |v_k|^2</math> 

Ad t igan, 

<math>|u_1\bar{v}_1 + \cdots + u_n \bar{v}_n|^2 \leq (|u_1|^2 + \cdots + |u_n|^2) (|v_1|^2 + \cdots + |v_n|^2)</math> 

==Amawal==
<div style="column-count:4;-moz-column-count:3;-webkit-column count:">
*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 
</Div>

== Isaɣuln ==
<references />{{Aggur:Tusnakt/Tin imgradn}}

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