
codomaine

ganithashaasthrathil, oru functionte codomaine allengil lakshyasthaanathinte koottam ennathu functionte ellah aouttputtum veezhunnathinu parimithappedutthiyirikku oru koottamaanu. ithu notteshanile settaanu. rench enna padam chilappol avyakthamaayi oru functionte codomaine allengil imej soochippikkaan upayogikkunnu.
domaine" ennu vilikkunna triple, athinte "codomaine", athinte "graph" enningane nirvachichaal oru codomaine oru functionte bhagamaanu. domaininte gadakangalkku mukalilulla roopathinte ellah gadakangaludeyum koottatthe "imej" ennu vilikkunnu. oru functionte chithram athinte codomaininte oru upavibhagamaanu, athinaal athu athumaayi poruthappedanamennilla. athaayath, surjective allatha oru functionil athinte codomainil gadakangalundu, athinu samavaakyathin pariharamilla.
oru graph ennu maathram nirvachichaal oru codomaine oru functionte bhagamalla. udaaharanathinu, settu sidhaanthathil oru functionte domaine sariyaaya klasai anuvadikkunnathu abhikaamyamaanu, eee saahacharyathil aupachaarikamaayi triple ennonnilla. atharam nirvachana pravarthanangalkku oru codomaine illengilum chila rachayithakkal ippozhum roopathil oru function avatharippichathinu sheshavum anoupachaarikamaayi ithu upayogikkunnu.
udaaharanagal.
oru pravarthanatthinaayi
nirvachichirikkunnathu
formula _ 4 aanu codomaine, pakshe oru negatteevu samkhyayilekkum mapp cheiyunnilla. 
athinaal chithram settu formula _ 5; i aanu.iii., edavela.
oru badal function ingane nirvachikkappedunnu 
ore samkhyaykku nalkiyittulla oru mapp cheyyumbol, eee kazhchappadil, avaykku vyathyastha codomainukal ullathinaal avaa ore pravartthanamalla. enthukondaanennu theliyikkaan moonnaamathe functione nirvachikkaam
domaine formula _ 9 aakaan kazhiyilla, pakshe formula _ 5 aayi nirvachikkaam
rachanakal soochippikkunnu
parisodhana nadathumbol athu upayogapradamalla. mattuvidhathil nirvachichillenkil, chithram ariyilla ennathu sariyaanu; ithu formula _ 4-nte oru upavibhaagamaanennu maathrame ariyoo. eee kaaranathaal, ithu samyojippikkumbol, outtputtu nirvachikkappedaatha oru aargyument labhichekkaam-negatteevu nambarukal domaininte gadakangalalla, athu square root functionaanu.
athinaal oru gadanayude valathuvashathulla functionte "codomaine" (athinte "imej" allah, ithu functionte anantharafalamaanu, koodaathe gadanayude thalatthil anjjaathamaayekkaam) idathu vashathulla functionte domaininte oru upavibhaagamaayirikkumbol maathrame function composition upayogapradamaakoo.
oru function sarjakshan aano ennu codomaine badhikkunnu, athil athinte codomaine athinte prathichaayaykku thulyamaanengil maathram function surjective aanu. udaaharanathil, oru sarjakshan aanenkilum allah. oru function oru kuthivayppaano ennathine codomaine baadikkunnilla.
codomaynum chithravum thammilulla vyathyaasathinte randaamathe udaaharanam rund vekttar speysukal thammilulla rekheeya parivarthanangalaanu-prathyekichu, formula _ 15 ll ninnu thannilekkumulla ellah rekheeya parivartthanangalum, yadhaartha gunakangalulla maatriksukalkk prathinideekarikkaan kazhiyum. oro matrix domaine formula _ 15, codomaine formula _ 15 ennivayulla oru bhoopadatthe prathinidheekarikkunnu. ennirunnaalum, chithram anishchithathvathilaanu. chila parivarthanangalkku muzhuvan codomaynum (eee saahacharyathil raankulla maatriksukal) thulyamaaya chithram undayirikkaam, ennaal palathum illa, pakaram chila cheria subspacilake (rank allengil ulla maatriksukal) mapp cheiyunnu. udaaharanathinu nalkia matricks edukkuka
ithu pooyint mapp cheiyunna oru rekheeya parivartthanatthe prathinidheekarikkunnu. formula _ 15 ll ninnu formula _ 15 lekkulla rekheeya parivarthanangalkku vyakthamaaya prasakthiyullathinaal pooyint chithratthil illa, pakshe ippozhum codomainil aanu. ellah matrixukaleyum pole, aaa settile oru amgathe prathinidheekarikkunnu. chithravum codomaynum thammilulla vyathyaasangal parishodhikkunnath palappozhum samshayaaspadamaaya functionte gunangal kandethunnathinu upayogapradamaakum. udaaharanathinu, muzhuvan codomainilum ullathinekkaal cheruthaanu athinte chithram ennathinaal poornna rank illennu nigamanam cheyyaam.

