compan vishleshanatil relecha bhag

relehcha bhag haah bahu-degree-auph-friedam compan pranalichya naisargik varanvartecha andaj lavnyasathi eka drut paddhat darshavito, jyamadhye vastuman aanee kadakpana matricks dnyat aahet.
formchya samanya pranalisathi eigenvalue samasya
sootra _ 1
olava naan aalyane aanee bahya shakti qamee hotat
sootra _ 2
mageel samikaran khalilpramane dekhil lihile jaau shakateh
sootra _ 3
jethe sootra 4, jyamadhye sootra 5 naisargik varanvarteche pratinidhitva karate, m aanee k heey anukrame vastavik sakaratmak samamiteey vastuman aanee kathorata matricks aahet.
aine"-degree-auph-friedam pranalisathi samikaranamadhye "aine" upay sootra _ 6, sootra _ 7 aahe jeey samikaran purn karate.
sootra _ 8
samikaranachya donhi bajunna sootra _ 9 neey gunakar karoon aanee scalar sootra _ 10 neey bhag deuun, igenvaluechy samasya khalilpramane vyakt karane shakya aaheh
sootra _ 11
sathee.
mageel samikaranat heey dekhil nirikshan karane shakya aahe qee ansh sambhavya urjechya pramanat aahe tarr vibhajak gatij urjeche mojmap darshavito. shivay, samikaran aaplyala naisargik varanvarta mojanyachi parvanagi dete, jarr eigenwector (tasech itar konatehi visthapan vector) sootra _ 12 dnyat asel tarach. shaikshanik hitsambandhansathi, jarr model vector mahit nastil, tarr aapan vareel prakriyechi punaravrutti karoo shakato parantu formula _ 13 aanee formula _ 14 neey anukrame formula _ 15 aanee formula _ 12 chee jaaga ghetali aahe. asey karoon aapan scalar sootra _ 17 midvato, jyala railays bhagfal asehi mhanatatah
sootra _ 18
mhanoon, relecha bhag haah eka scalar aahe jyache moolya vector sootra _ 14 varr avalambun asate aanee joparyant teey model vector sootra _ 21, "i" = 1,2,3 pasoon vajviritya door aahe toparyant konatyahi aniyantrit vector sootra _ 14 sathee changlya andajane tyachi ganana kelee jaau shakate.., aine.
kaaran, heey sangane shakya aahe qee vector sootra _ 14 heey pratham kramachya thodya pramanat model vector sootra _ 7 peksha vegale aahe, tyamule relechya bhagacha yogya parinam andajit pramanapeksha sanvedansheelpane vegala nasel aanee mhanunach hii paddhat khoop upayukt tharate. sarvat qamee model vector sootra _ 24 chaa andaj lavnyacha eka changla marg, jeey samanyatah bahutek sanrachanansathi changle karya karate (jaree hummy dilee jaat nasali taree), teey mhanje _ 24 heey sootra, jyache vikarn vastuman matricks atinche samaan sapeksh vitaran asalelya lagoo kelelya balatoon sthir visthapanachya barobariche aahe asey gruheet dharane. pudhil 3-udaharanadvare nantarche spasht kele jaau shakate.
udaharan-3 dof.
udaharanadakhal, aapan 3-degree-auph-friedam pranalicha vichar karoo shakato jyamadhye tyanche vastuman aanee kadakpana matricks khalilpramane olakhale jaatatah
sootra _ 26
sarvat qamee naisargik varanvartecha andaj ghenyasathi aapan vastumananchya pramanat bull pranalila bharit karoon midavalelya sthir visthapanacha chachani vahak nivadatoh
sootra _ 27
asha prakare, chachani vahak hoil
sootra _ 28
jyamule aaplyala relehcha bhagank mojata yetoh
sootra _ 29
asha prakare, relechya bhagankadware mojali jaanari sarvat qamee naisargik varanvarta ashee aaheh
sootra _ 30
ganana sadhan vaparane heey "vastavik" sadhanapeksha kitee vegale aahe heey padtalnyasathi khoop jalad aahe. yaa prakaranat, matalyabcha vapar karoon, heey mojale gele aahe qee sarvat qamee naisargik varanvarta aaheh sootra _ 31 jyamule relehche andaje vaparoon sootra _ 32 madhye truti aalee aahe, haah eka ullekhaneey parinam aahe.
relecha bhagank sarvat qamee naisargik varanvartecha achook andaj lavnyas kassa saksham aahe heey udaharan darshavate. sthir visthapan vectorcha chachani vector mhanoon vapar karanyachi pratha vaidh aahe kaaran sthir visthapan vector sarvat qamee compan paddhatishi samya thevato.

