
frobenius siddhaantam (vaastava vibhajana algibras)

ganita saastramlo, marinta pratyaekamgaa nairoopya beejaganitamlo, 1877loe ferdinand georg frobenius niroopinchina frobenius siddhaantam, vaastava sankhyalapai parimita-dimensional associative division algibralanu vargeekaristundi. siddhaantam prakaram, atuvanti prati beejaganitam eee krindi vaatilo okadaaniki isomorphicga untundih
eee algibralu varusaga nijamaina parimaanaanni kaligi untaayi. eee moodu algibralalo, mariyu parivartanaseelamainavi, conny kaadu.
rujuvu.
eee krindi rujuvuku pradhana amsaalu kylie-hamilton siddhaantam mariyu beejaganitam yokka praathamika siddhaantam.
daavaa.
eee vaadanaku keelakam eee krindi vidhamgaa undhi
daavaa rujuvu oka-vector space yokka parimaanamgaa undanivvandi, mariyu lakshana bahupadamtho enchukondi. beejaganitam yokka praathamika siddhaantam dwara, manam vraayavacchu
manam bahupadula paramgaa tirigi vraayavachuhu
endukante, bahupadaalu annee irreducible ovar. kylie-hamilton siddhaantam prakaram, mariyu idhi vibhajana beejaganitam kabatti, idhi kontamandiki ledhaa kontamandiki daanini anusaristundi. modati kesu adhi nijamani suuchistumdi. rendava sandarbhamlo, idhi kaneesa bahupadi. endukante kaneesa bahupadi vale adhe sanklishta muulaalanu kaligi untundi mariyu idhi vaastavamainadi kabatti adhi anusaristundi
endukante inn yokka gunakam yokka lakshana bahupadi oka sanketam varaku untundi. anduvalla, manamu paina perkonna sameekaranam nundi chaduvutamu unte mariyu matrame unte, maroe maatalo cheppalante unte mariyu matrame unte.
alaage annintikee upasamiti. mukhyamgaa, idhi vector subspace. rank-shoonyata siddhaantam appudu suutram _ 5 yokka kernell ayinanduna daaniki parimaanam undani suuchistumdi. endukante avi vidadeeyabadi untaayi (i.ii. avi suutram _ 6) nii santruptiparustaayi, mariyu vaati kolatalu mottam, manaku adhi undhi.
mugimpu.
nirvachinchadaaniki. gurtimpu kaaranamgaa, adhi nijamainadani anusaristundi. inca, endukante, manaku undih kosam. eee vidhamgaa idhi saanukuula khachitamaina samaroopa dvimukha roopam, maroe maatalo cheppalante, oka antargata utpatti.
beejaganitamgaa utpatti chese daani yokka upasthanamgaa undanivvandi mariyu eee lakshanaaniki sambandhinchi idhi chaalaa takkuvagaa untundi. dheeniki sambandhinchi oka orthonormal praatipadikagaa undanivvandi. appudu orthonormality suchistundihi
okavela, appudu isomorphic.
okavela, appudu sambandham dwara utpatti cheyabadutundi mariyu daaniki lobadi untundi. anduvalla idhi isomorphic.
okavela, idhi sambandhaalaku lobadi utpatti cheyabadinadi paina choopabadindi 
ivi khachitamgaa sambandhaalaki sambandhinchinavi.
okavela, appudu vibhajana beejaganitam kakapovachhu. anie anukundam. veelu. adhi chudatam sulabham (idhi panichesthe matrame). vibhajana beejaganitam ayithe, suuchistumdi, dheeni ardham avtundi mariyu utpatti chestundi. idhi kaneesatvaaniki viruddhamgaa untundi.

