Aljibṛ imzireg
-
yiwet talɣa n aljibṛ imzireg
Awal Amatu
ẓreg'''Aljibṛ imzireg''' d uḥric deg tusnakt i d-yeɛnan tallunt tamawayt akked alsileɣ imzireg, agtalɣa tamatut n tiẓriwin n inagrawen n tigda timzirigin.
Amezruy
ẓregAljibṛ 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)
ẓregs 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
ẓregAljibṛ 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
ẓreg
- 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
ẓregaljibṛ 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
ẓreg| taqbaylit | tafransist | taɛrabt |
|---|---|---|
| aljibṛ imzireg | Algèbre linéaire | الجبر الخطي |
| Tallunt tamawayt | Espace vectoriel | فضاء شعاعي |
| Alsileɣ imzireg | Transformation linéaire | تحويل خطي |
| Agtalɣa | Formalisation | تشكيل |
| Anagraw | Système | نظام |
| Tigda timzirigin | Équations linéaires | معادلات خطية |
| Afnaẓ igensenlɣan | Réduction d'endomorphisme | اختزال التشكل الذاتي |
| Takuẓt | Quaternion | رباعي |
| Amaway | Vecteur | متجه |
| Aɣan | Traité | معاهدة |
| Igejdiwen | Axiomes | بديهيات |
| Asnasen imzirgen | Applications linéaires | تطبيقات خطية |
| Tallunt tanzeggit | Espace géometrique | فضاء هندسي |
| Taɣda | droite | مستقيم |
| Agni | Plan | مستوى |
| Tallunt taɣarant | Espace physique | فضاء فيزيائي |
| Tamṣukt | Structure | بنية |
| Tazmilt | Notion | مفهوم |
| Tagrumma | Ensemble | مجموعة |
| Agraw | Groupe | زمرة |
| Azebg | Anneau | حلقة |
| Tafekka | Corps | جسم |
| Tanzeggit taneẓlayt | Géométrie différentielle | هندسة تفاضلية |
| Tallunt takaṛtizit | Espace cartésien | فضاء ديكارتي |
| Igazen | points | نقاط |
| Almessi asaraw | famille génératrice | |
| Almessi ilelli | famille libre | |
| Azadur | base | أساس |
| Tallunt tasint | Espace dual | فضاء ثنائي |
| Tasmekta | Cardinal | عدد ترتيبي |
| Tidullanin | Sous-espaces | فضاءات جزئية |
| Tanfalit | Formule | صيغة |
| Amsedɣidis | Parallélogramme | متوازي أضلاع |