matricks farak samikaran

matricks farak samikaran heey eka farak samikaran aahe jyamadhye matrixcha vapar karoon eka velee eka variableschya vectorche (kinwa kadhikadhi, matricks) moolya tyachya swatachya moolyashi sambandhit asate. samikaranacha kram mhanje chull sadishchya konatyahi done darshavilelya mulyanmadhil kamal veleche antar. udaharanarth,
heey mool kramankachya matricks farak samikaranache eka udaharan aahe, jyamadhye variablescha vector aahe aanee matricks aahet. heey samikaran eksandh aahe kaaran samikaranachya shevati konatihi vector sthirank sandnya jodali jaat nahee. tech samikaran asey dekhil lihile jaau shakate 
kinwa 
sarvat samanyatah aadhalanari matricks farak samikarane hii pratham-kram aahet.
naun homogenous first aurder cases aanee sthir sthitee.
eksandh pratham-kram matricks farak samikaranache eka udaharan aahe
yojak sthir vectors. yaa pranalichi sthir sthitee hii vectorchi moolya aahe, jee gathali gelee tarr nantarpasoon vichalit honar nahee. farak samikaranat seet karoon aanee midvinyasathi nirakaran karoon shodhale jaate
olakh matricks kuthe aahe aanee jithe asey gruheet dharale jaate qee teey ulat karata yenyajoge aahe. mug sthir avasthepasoonchya vichalananchya drushtine gair-samaroop samikaran samaroop swarupat punha lihile jaau shakateh
pratham-kramankachya prakaranachi sthirata.
pratham-kram matricks farak samikaran sthir aahe-mhanje, sankraman matrixchya serve eigenvaluesche (vastavik kinwa jatil asso) nirpeksh moolya 1 peksha qamee asel tarach teey sthir sthiteet lakshanrahitpane ekatra yete.
pratham-kram prakaranacha upay.
asey gruheet dhara qee samikaran eksandh swarupat thewale gele aahe. mug aapan prarambhik sthitimadhun varanvar punaravrutti aanee paryay karoo shakato, jeey vectorche prarambhik moolya aahe aanee jeey samadhan shodhanyasathi mahit asane aavashyak aaheh
aanee asha prakare, jenekarun ganiteey preranadvare yache uttar aahe
pudhe, jarr karnarekheey asel tarr aapan tyache aaygan moolya aanee igenvectorchya sandarbhat punha lihu shakato, jyache uttar asey aahe
jethe eka matricks aahe jyache stambh heey eigenwector aahet (eigenvalues serve bhinn aahet asey gruheet dharoon) aanee eka vikarn matricks aahe jyache vikarn ghatak eigenvalues aahet. heey samadhan vareel sthiratechya parinamala prerit karateh jarr aanee jarr serve eigenvalues sampoorn mulyatil ektepeksha qamee asateel tarach kalantarane shoonya matrixver sankuchit hote.
pratham-kram matricks pranalitoon ekach scalar chalchi gatishilata kadhane.
- dimensional pranalipasoon suruvat karoon, aapan steet variablespacky ekachi dynamics kadhu shakato, samaja. vareel samadhan samikaran darshavite qee yache uttar eigenvaluechya drushtine aahe. mhanoon utkrantiche varnan varnan samikaranamadhye tyach eigenvaluescha samavesh asalele samadhan asane aavashyak aahe. heey varnan antardnyanane utkrantiche samikaran prerit karate, jeey aahe
jethe parameters matrixchya vaishishtyapurn samikaranatun aaheth
asha prakare, aayami pratham-kram resheey pranaliche pratyek vaiyaktik scalar chull eka eka-bhinn th-degree farak samikarananusar vikasit hote, jyacha sthirata gunadharm (sthir kinwa asthir) matricks farak samikaranapramanech asato.
uchch-kramatil prakarananche nirakaran aanee sthirata.
uchch kramache matricks farak samikarane-mhanje, eka kalavadhipeksha jaast kalavadhisah-sodavali jaau shakatat aanee block matricks (matrixche matricks) vaparoon tyanna pratham-kramachya swarupat rupantarit karoon tyanchya sthirateche vishleshan kele jaau shakate. udaharanarth, samaja aaplyakade mool kramankache samikaran aahe.
chull vector asane aanee asane. heey formmadhye stack kele jaau shakate
olakh matricks kuthe aahe aanee shoonya matricks kuthe aahe. tyanantar current aanee ekada-lagg kelelya chalanche stack kelele vector aanee block matricks darshavitana, aamchyakade aadhipramanech samadhan aahe 
jarr matrixchi serve eigenvalues nirpeksh mulyatil ektepeksha lahan asateel tarach heey stacked samikaran aanee asha prakare mool mool kramankache samikaran sthir asate.
nonlinear matricks difference samikaraneh ricati samikarane.
resheey-chaturthansh-gossian niyantranat, vartaman aanee bhavishyatil kharchachya "matricks" chya ulat utkrantisathi eka araikhik matricks samikaran udbhavate, jeey khalee darshavile aahe. yaa samikaranala swatantra gatishil ricati samikaran mhanatat aanee jevha resheey matricks farak samikarananusar vikasit honara chull vector, dvighat kharch karya anukool karnyasathi bahya vectormadhye ferfar karoon niyantrit keela jaato tevha teey udbhavate. heey ricati samikaran khaleel kinwa tatsam swaroop dharan karateh
jethe, aanee aahet, mhanje, niyantrit kele jaanare vectormadhil ghatakanchi sankhya aahe aanee niyantran vectormadhil ghatakanchi sankhya aahe. parameter matricks aanee resheey samikaranatil aahet aanee parameter matricks aanee vargvari kharch karyatil aahet. tapashilansathi yethe pahaa.
sarvasadharanpane heey samikaran vishleshanatmakaritya sodavale jaau shakat nahee; tyaeivaji, mulyancha kram ricati samikaranachi punaravrutti karoon aadhalato. tathapi, heey darshavile gele aahe qee heey ricati samikaran vishleshanatmakaritya sodavale jaau shakate, jarr teey scalar rational difference samikaranat qamee kele tarr; shivay, konatyahi aanee jarr sankraman matricks ekarsatmak nasel tarr ricati samikaran matrixchya eigenvaluechya sandarbhat vishleshanatmakaritya sodavale jaau shakate, jaree heey sankhyatmakdrushtya shodhane aavashyak asale taree. 
bahutek sandarbhanmadhye, kalantarane mage sarkanyachi utkranti sthir asate, mhanje tee eka vishisht nishchit matrixmadhye rupantarit hote jee itar serve matricks tarksangat asali tarihi atarkik asoo shakate. hehee pahaa.
sambandhit ricati samikaran aahe
jyamadhye serve matricks aahet. heey samikaran spashtapane sodavale jaau shakate. samaja sootra 17 jeey nishchitpane sobat aanee barobar aahe. mug heey farak samikaranat vaparoon utpann milate 
mhanoon, form formula _ 19 heey sarvansathi samavisht aahe. mug utkranti aanee asey lihile jaau shakate 
asha prakare preranadvare

