
kaneesa bahupadi (leanier algibra)

leanier algibralo, oka kshetrampai oka maatruka yokka kaneesa bahupadi anedi athi takkuva degree unna monic bahupadi. edainaa itara bahupadi anedi a (bahupadi) gunakam.
eee krindi moodu prakatanalu samanamga untayih
oka moolamu yokka gunakaaram anedi "khachitamgaa" kaligi unna atipedda shakti. maroe maatalo cheppalante, ghaataankaanni penchadam valla marinta pedda kernels vastaayi, conny ghaataankaanni marinta penchadam valla adhe kernell vastundi. adhikarikamga, idhi nilpotent suuchika.
kshetram beejaganitaparamgaa moosiveyakapothe, appudu kaneesa mariyu lakshana bahupadaalu vaati muulaala (inn) prakaram matrame karakalu avasaram ledhu, maroe maatalo cheppalante avi degree kante ekkuva irreducible bahupadi kaarakaalanu kaligi undavacchu. irreducible bahupadulaku okadaaniki saaruupya samaanatvaalu untayih
lakshana bahupadi vale, kaneesa bahupadi bays feeled meeda aadharapadi undadu. maroe maatalo cheppalante, pedda feeldlo gunakaalu unna matricksnu pariganinchadam valla kaneesa bahupadi maaradu. dheeniki kaaranam vilakshanhamaina bahupadi (idhi nirnayakaala nirvachanam nundi takshaname unna chota) vishayamlo bhinnamgaa untundi, antey kaneesa bahupadi anedi eee saktula madhya sarala aadharapadatam yokka sambandhaala dwara nirnayinchabadutundih bays feeldnu vistarinchadam atuvanti kotta sambandhaalanu parichayam cheyadu (ledhaa idhi ippatike unna vaatini tolaginchadu).
kaneesa bahupadi tarachugaa lakshana bahupadi vale untundi, conny ellappuduu kaadu. udaaharanaku, identity matricks yokka multiple ayithe, daani kaneesa bahupadi kernell ippatike mottam space ayinanduna; marovaipu daani lakshana bahupadi (ekaika aigen value, mariyu lakshana bahupadi yokka degree ellappuduu space yokka dimensionku samanamga untundi). kaneesa bahupadi ellappuduu lakshana bahupadaanni vibhajistundi, idhi kylie-hamilton siddhaantaanni roopondinchadaaniki oka maargam (oka kshetrampai maatrikala vishayamlo).
adhikaarika nirvachanam.
oka kshetrampai parimita-dimensional vector sthalampai endomorphism ichinatlayithe, sett ilaa nirvachinchabadaali
kshetrampai anni bahupadula sthalam ekkada undhi. idhi saraina aadarsam. oka feeled kabatti, idhi oka pradhana aadarsha domine, anduvalla edainaa aadarsam oke bahupadi dwara utpatti cheyabadutundi, idhi oka unit varaku pratyekamainadi. generatorlalo okati monic kabatti generatorlalo oka nirdishta empika cheyavachu. kaneesa bahupadini utpatti chese monic bahupadigaa nirvachistaaru. idhi athi takkuva degree kaligina monic bahupadi.
applications.
oka kshetrampai parimita-dimensional vector space yokka endomorphism daani kaneesa bahupadi karakalu puurtigaa "vilakshanhamaina" sarala karakalaga maarinatlayithe matrame vikarnam avutundi. prati aigen valueki oke oka amsam matrame untundi antey saadhaarana igenspace igenspace kii samanamga untundih prati jordan block parimaanaanni kaligi untundi. marinta saadhaaranamgaa, vibhina sarala karakalalo karakalu unde bahupadi sameekaranaanni santruptiparichinatlayite, adhi vikarnamgaa untundih daani kaneesa bahupadi anedi oka bhagakam, anduvalla vibhina sarala karakalalo karakalu kooda. mukhyamgaa okati kaligi untundih
eee kesulanu neerugaa niroopinchavacchu, conny kaneesa bahupadi ekikruta drukpatham mariyu rujuvunu istundi.
ganana.
nirvachinchina sunna kaani vector kosamh
eee nirvachanam saraina aadarsam yokka lakshanaalanu santruptiparustundi. daanini utpatti chese monic bahupadigaa undanivvandi.
udaaharana.
praamaanika praatipadikana, matricks thoo endomorphism gaa nirvachinchandi,
modati canonical basis vector mariyu daani punaraavruta chitraalanu okadaani dwara teesukovadam dwara pondavacchu
veetilo modati moodu saralamgaa swatantramgaa sulabhamgaa kanipistaayi, anduvalla annintinee vistarinchi untaayi. chivaridi tappanisarigaa modati moodinti sarala kalayika, vaastavaaniki
tadwarah 
idhi vaastavaaniki kaneesa bahupadi mariyu lakshana bahupadi & hair sp;: vaastavaaniki vibhajistundi, mariyu modati mariyu chivari degreelu mariyu annee monic ayinanduna, avanni okela undaali. maroka kaaranam emitante, saadhaaranamgaa edainaa bahupadi oka vektarnu naasanam chesthe, adhi kooda naasanam avutundi (adhi naasanam avtundani cheppe sameekaranaaniki vartistundi), anduvalla punaraavrutam dwara idhi punaraavruta chitraala dwara utpatti cheyabadina mottam sthalaanni naasanam chestundi; prastuta sandarbhamlo aaa sthalaaniki mottam anie manam chushamu. nijaaniki sunna maatrika ayina puurti maatrika kosam okaru dhruvikaristaruhu