
thet resheey parivartan

jethe sootra _ 3 aanee sootra _ 4 dnyat vahak aahet, sootra _ 5 adnyat scalar gunakaraparyant samanata darshavate aanee sootra _ 6 haah eka matricks (kinwa resheey parivartan) aahe jyamadhye nirakaran karnyasathi adnyat asatat.
yaa prakarcha sambandh prakshepak bhoomitimadhye varanvar disun yeto. vyavharik udaharananmadhye ekhadya drushyatil 3dii bindu aanee pinhole cameachya pratimechya pratalavaril tyanche prakshepan yanchyatil sambandh aanee samalekhan yancha samavesh hoto.
parichay.
resheey samikarananchi eka samanya pranali
udaharanarth, matricks samikaran sootra 9 mhanoon punarlekhan karoon sodavale jaau shakate, jethe matricks sootra 10 aanee sootra 11 madhye tyanchya sambandhit stambhanmadhye vector sootra 3 aanee sootra 4 asatat. eka adviteey upay astitvat asalyane, too yaa dware deela jaato
samikarane purn kinwa qamee nirdharit jhalyas dekhil upayanche varnan kele jaau shakate.
thet resheey parivartanachi samasya vareel pramanit prakaranapeksha vegali karnari gosht mhanje paribhashit samikaranachya davya aanee ujavya bajoo adnyat gunak ghatkadvare bhinn asoo shakatat, joou "keey" varr avalambun asato. parinami, manak prakaranapramane sootra _ 6 chee ganana kelee jaau shakat nahee. tyaeivaji, samanata sambandh yogya resheey sajatiy samikarane mhanoon punarlikhit kele jaatat jee nantar manak paddhatidvare sodavali jaau shakatat. samaan samikarane eksandh resheey samikarane mhanoon punha lihine aanee manak paddhatinni tyanche nirakaran karane yaa sanyojanas thet resheey parivartan algoridam kinwa dii. ell. tii. algoridam asey mhanatat. dii. ell. tii. chey shrey ivan ess. ess. doubleu. laa dile jaate.
udaharanadakhal.
samaja sootra 16. sootra 17 aanee sootra 18 heey done dnyat vahak asoo dya aanee aaplyala sootra 19 matricks sootra 6 asey shodhayache aahe qee
jethe sootra _ 22 haah "k" samikaranashi sambandhit adnyat scalar ghatak aahe.
adnyat scalerpasoon mukt honyasathi aanee eksandh samikarane midvanyasathi, samamiteey-virodhi matricks paribhashit qaraa.
aanee samikaranachya donhi bajunna davikadoon sootra _ 24 neey gunakar qaraa.
sootra _ 26 pasoon khaleel eksandh samikarane, jyat aata adnyat scalar naheet, tee hatat aahet.
samikarananchya yaa sanchatoon sootra _ 6 sodavanyasathi, vector sootra _ 3 aanee sootra _ 4 aanee matricks sootra _ 6 chya ghatakancha vichar karah
aanee vareel eksandh samikaran banate
heey matrixchya swarupat dekhil lihile jaau shakateh
jethe sootra _ 39 aanee sootra _ 40 heey donhi 6-aayami vahak aahet, jyachi vyakhya ashee kelee jaateh
aataparyant, aaplyakade 1 samikaran aanee 6 adnyat aahet. eksandh samikaranancha sanch matrixchya swarupat lihila jaau shakato.
jethe sootra _ 44 heey eka sootra _ 45 matricks aahe jeey dnyat vector sootra _ 39 tyachya ranganmadhye dharan karate. adnyat sootra _ 40 nirdharit kele jaau shakate, udaharanarth, sootra _ 44 chya ekvachan mulyachya vighatanadvare; sootra _ 40 heey sootra _ 44 chey ekvachan moolyashi sambandhit ekvachan vector aahe jeey shoonyachya barobariche aahe. ekada sootra _ 40 nishchit jhaale qee, matricks sootra _ 6 chey ghatak vector sootra _ 53 pasoon punha vyavasthit kele jaau shakatat. lakshat ghya qee sootra _ 40 kinwa sootra _ 6 chey scaling mahatvache nahee (teey shoonya nasalele asale pahije heey vagalata) kaaran paribhashit samikarane aadhich adnyat scalingsathi parvanagi detat.
vyavharat vector sootra _ 3 aanee sootra _ 4 madhye aavaj asoo shakato jyacha arth assa aahe qee samanata samikarane keval andaje vaidh aahet. parinami, eka sadish sootra _ 40 asoo shakat nahee jeey eksandh samikaran sootra _ 43 nemke sodavate. yaa prakarananmadhye, sootra _ 61 chya sarvat lahan ekvachan moolyashi sambandhit eka ekvachan vector mhanoon sootra _ 40 nivadoon ekoon kiman chauras samadhan vaparale jaau shakate.
adhik samanya prakarane.
vareel udaharanamadhye sootra _ 62 aanee sootra _ 63 aahe, parantu samanata sambandhanna eksandh resheey samikarananmadhye punha lihinyasathiche samanya dhoran sootra _ 3 aanee sootra _ 65 yaa donhisathi aniyantrit parimananmadhye samanyikrut kele jaau shakate.
jarr sootra _ 62 aanee sootra _ 67 asel tarr mageel abhivyakti ajunahi samikaranakade neuu shakatat.
jethe sootra _ 6 aata sootra _ 71 aahe, pratyek "keey" sootra _ 6 chya _ 72 adnyat ghatakanmadhye eka samikaran pradan karate aanee ektritpane hii samikarane dnyat sootra _ 75 matricks sootra _ 44 aanee adnyat "2 kyu"-aayami vector sootra _ 77 sathee sootra _ 74 lihili jaau shakatat, haah vector purvipramanech aadhalu shakato.
sarvat samanya cases formula _ 78 aanee formula _ 67 madhye. purvichya tulanet mukhya farak mhanje matricks formula _ 80 aata formula _ 81 aanee anty-cemetric aahe. jevha sootra _ 82 asha matrixchi jaaga aata eka-aayami nasate, tevha tee parimanachi asate.
yacha arth assa qee "keey" chey pratyek moolya yaa prakarchi "emm" eksandh samikarane pradan karate
jethe sootra _ 87 haah sootra _ 81 samamiteey-virodhi matrixchya jaagecha "m"-aayami aadhar aahe.
udaharanadakhal "pii" = 3.
jarr "pii" = 3 asel tarr khaleel teen matricks sootra _ 87 nivadle jaau shakate.
yaa vishisht prakaranat, eksandh resheey samikarane ashee lihili jaau shakatat
jethe sootra _ 95 heey vector cross productche matricks pratinidhitva aahe. lakshat ghya qee heey shevatche samikaran vector moolya aahe; davikadil bajoo hii _ 96 yaa sutratil shoonya ghatak aahe.
k" chey pratyek moolya sootra _ 6 chya adnyat ghatakanmadhye teen eksandh resheey samikarane pradan karate. tathapi, sootra _ 95 madhye kram = 2 asalyane, jastit jaast done samikarane reshiyadrushtya swatantra aahet. vyavharat, mhanoon, teen matricks sutranpaiki fakt done sootra _ 87 vaparane samanya aahe, udaharanarth, "m" = 1,2 sathee. tathapi, samikarananmadhil resheey avalambitva sootra _ 3 varr avalambun aahe, jyacha arth assa aahe qee durdaivane prakarananmadhye, udaharanarth, "m" = 2,3 nivadane changle asate. parinami, samikarananchi sankhya chintechi baab nasel tarr, matricks sootra _ 44 tayar jhalyavar tinhi samikarane vaparane changle asoo shakate.
parinami tayar honanya sajatiy resheey samikarananmadhil resheey avalambitva hii "pii"> 2 prakaranasathi eka samanya chinta aahe aanee ektar samamiteey-virodhi matricks sootra _ 87 chaa sanch qamee karoon kinwa sootra _ 77 nirdharit karnyasathi sootra _ 44 laa aavashyakatepeksha mothe honyas parvanagi deuun hatalale pahije.