Aljibṛ imzireg

Awal Amatu 
'''Aljibṛ imzireg''' d uḥric deg tusnakt i d-yeɛnan tallunt tamawayt akked alsileɣ imzireg, agtalɣa tamatut n tiẓriwin n inagrawen n tigda timzirigin.

 Amezruy 
Aljibṛ imzireg tebda-d sɣur amusnak afarsi AL Xawarizmi, i d-yewwi tikti sɣur iḍrisen n ihendiyen d yesmed imahilen n uɣerbaz agrigi aqbur.

Aṭas n imusnaken i nudan ɣef taɣult agi syin am René Descartes s wuguren n tanzeggit-ines, Jean d'Alembert s tiffin-ines "amguccel".

Aljibṛ imzireg ur yuɣal d afurk iman-is deg tusnakt alamma d tasut tis 19. Deg tallit-a, aṭas n yimusnawen fkan-d timerniyin meqqren:

 Carl Friedrich Gauss (1777-1855): Yufa-d tarrayt tamatut i ufran n yinagrawen n tigda imziragen. Gauss d amusnak almani yettwassnen s waṭas s tigmiyin-is deg tusnakt.
 Camille Jordan (1838-1922): Yefra-d ugur n ufnaẓ igensenlɣan. Jordan d amusnak afransis yettwassnen s uxeddim-is deg aljibṛ d tanzeggit.
 William Rowan Hamilton (1805-1865): Deg useggas 1843, yufa-d Takuẓt (quaternion). Hamilton d amusnak irlandi, d netta i d-yesnulfan awal "vector" (s taqbaylit "amaway").
 Hermann Grassmann (1809-1877): Deg useggas 1844, yessufeɣ-d aɣan-is "Die lineale Ausdehnungslehre" (tiẓri n usiɣzef imzireg). Adlis-a d tikli tamezwarut i uselɣu amatu n tezmilt n tallunt tamawayt. Ɣas akken ur yettwassen ara aṭas deg tallit-is, aɣas-a yegber tuget n tektiwin titrarin n aljibṛ imzireg. Grassmann d amusnak almani.

 Giuseppe Peano (1858-1932): Deg useggas 1888, yefka-d igejdiwen (axiomes) ar tiẓriwin  s udem ummid. Peano d amusnak aṭelyani.

 Tanfa (intérêt) 
s talɣa-ines taḥerfit, isnasen imzirgen deg tallunin timawiyin (espaces vectoriels) ggensen asikel deg tallunin tinzegganin tiferdisin am taɣda, agni neɣ tallunt-nneɣ  taɣarant. tamṣukt tamirant n waljibṛ ad aɣ-teǧǧ ad nesmati tazmilt n tallunt ar tidda menwala.

Aljibṛ imzireg ag-teǧǧ ad nefru yal tagrumma n tugdiwin qqarasent timzirigin.

Tallunin timawiyin d nutni daɣen allal agejdan des tussniwin n ujenyuṛ akked yimahilen nniḍen.

deg taggara, Aljibṛ imzireg d allal deg tusnakt am tiẓriwin n "agraw","azebg", "tafekka", "tasleṭ  tamesɣant",  "tanzeggit taneẓlayt" neɣ deg tiẓri n "imḍanen"

 Asenked aferdisan 
Aljibṛ imzireg yebdu s tezrawt n imalayen deg tallunin tikaṛtiziyen n tisekta 2 ar 3. amaway, dagi, d tserkemt n  tegdazelt n sin igazen i yesdukklen iɣilen d taɣda i d-yettwaseknen s tiɣzi-nsen, tanila-nsen, anamud-nsen : sin igazen ggensen yiwen umalay ma  d akuẓdis i -d-yettwalɣen seg igazen si kuẓ yis-sen d amsedɣidis

 Kra n yisekkuden 

 asekkud n "azadur imettu" (base incomplète) : ad tili E d tallunt tamawayt, G d almessi  asaraw ma d L d almessi ilelli n ilawayen n E, ihi ma drus yella azadur n E yettwalɣa s uzdukkel n L akked amur n G.
 s umaẓlay, yal tallunt tamawayt tesɛa ma drus yiwen uzadur.
 yal izaduren n yiwet n tallunt tamawayt sɛant yiwet tasmekta (cardinal)
 yal tallunt tamawayt A tesɛa tallunt tasint (duale) A* ; ma A n tesmekta ifuken, A* netta daɣen yesɛa tasmekta-nni.
 Tanfalit n Grassmann: ad ilint F d G sin n tidullanin (sous-espaces) imawayen n yiwet tallunt tamawayt. Nesɛa ihi : 

 Asemres 
aljibṛ imzireg yettwasemres deg aṭas n wannaren 

 Tasnawalt: Deg uselɣu d usesfer n yisefka.
 Tasengama: Deg usegzi n yisekla d tkerḍiwin.
 Tussna n usihel: Deg uheggi n yinagrawen imziragen meqqren.
 Tasertit: Deg uslaḍ n tefranin d wansa n yimdanen.

 Tasnakant: Deg uheggi n yinagrawen n tegnit.

 Amawal 
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