
kaarttante maanadandam

ganithashaasthrathil, kaarttante maanadandam 0 enna swabhaavasavisheshathayilulla oru nuna beejaganitam pariharikkaavunna vyavasthakal nalkunnu, ithu nuna beejaganitam ardha lalithamayirikkunnathinulla anubandha maanadandatthe soochippikkunnu. ithu soothravaakyam nirvachicha formula _ 1-leeii samamita dvirekheeya roopamaaya killing roopathe adisthaanamaakkiyullathaanu.
ivide oru leanier oopparettarude adayaalathe tra soochippikkunnu. maanadandam avatharippichathu.
parihaarakshamathaykkulla kaarttante maanadandam.
parihaarakshamathaykkulla kaarttante maanadandam iprakaaramaanu
pariharikkaavunna kesil formula 4 ennathu lies sidhaanthathil ninnu pinthudarunna vasthuthayaan, athu graundu feeldinte beejaganita klosarinekkaal mukalile thrikonaakrithiyilulla roopathil formula 7 sthaapikkunnu (graundu feeld vipuleekaricha sesham trace kanakkakkaam). jordan-chevalli vighadanathe adisthaanamaakki nilpodansi maanadandatthil ninnu vipareetham kanakkakkaam (thelivinaayi, link pinthudaruka).
adjayint praathinidhyathinu kaarttante maanadandam prayogikkunnathu nalkunnu 
ardha lalithathaykkulla kaarttante maanadandam.
ardha lalithathaykkulla kaarttante maanadandam iprakaaramaanu
 oru parimitha-dimensional lye algibraikku (eathenkilum swabhaavathil) degenerate cheyyaatha inavariyant bilinear roopamundengil poojyamallaatha abelian idealukalillengil, prathyekichu athinte killing phoom degenerate allengil, athu lalithamaaya lye aaljibrakalude aakethukayaan ennathinu valare cheria thelivu nalki.
neremarichu, oru ardha lalithamaaya beejaganithathinu (swabhaavam 0 ll) oru degenerate allatha kola roopamundennu kaarttante parihaarakshamathayude maanadandatthil ninnu eluppathil pinthudarunnu.
udaaharanagal.
kaarttante maanadandangal swabhaava soothravaakyathil paraajayappedunnu; udaaharanathina
oru parimitha-dimensional lye aljibra nilpottant aanenkil, kolayali roopam thulyamaayi poojyamaanu (kooduthal saadhaaranayaayi kolayali roopam eathenkilum nilpottant idealil aprathyakshamaakunnu). neremarichu thettaanu kolayali roopam aprathyakshamaakunna nilpottant allatha nuna aaljibrakalundu. bii" nilpottant allaathathum "bii" enna endomorphisamaayi "vii" yill pravartthikkunna oru dimensional lye aljibrayullah oru abelian lye aljibra "vii" yude semidirect prodakt oru udaaharanam nalkunnu.
0 enna swabhaavathil, oro reductive lye aljibraykkum (abelian, lalithamaaya lye aaljibrakalude aakethuka) oru noonn-degenerate invariyant cemetric bilinear roopamundu. ennirunnaalum, vipareethamaayath thettaanu degenerate cheyyaatha invariyant cemetric bilinear roopamulla oru lye aljibra lalithavum abelian lye aaljibrakalude aakethukayaayirikkanamenni. oru saadhaarana counderexamble "g" = "l" ["t"] "t" "n" "l" ["t"] aanu, ivide "n"> 1 "," l "ennathu oru dvirekheeya roopamulla lalithamaaya sankeernamaaya lye beejaganithamaanu (,), koodaathe" g "leeii dvirekheeya roopam" c ["t"]-moolyamulla dvirekheeya roopathil "t" n "−1 nte gunakam" g "ll" l "enna roopathaal prachodippikkappettathanda. dvirekheeya roopam apachayamillaathathaanu, ennaal nuna beejaganitam lalithavum abelian nuna aaljibrakalude aakethukayalla.

