asambandhitata (sambhavyata siddhant)

sambhavyata siddhant aanee sankhyikimadhye, done vastavik-moolya yadruchchik chull, sootra _ 1, sootra _ 2, jarr tyanche sahparivartan, sootra _ 3, shoonya asel tarr teey parasparsambandhit naheet asey mhatale jaate. jarr done chull parasparsambandhit nastil, tarr tyanchyat konatahi resheey sambandh nahee.
jevha heey astitvat asate tevha, jevha konatyahi eka chalamadhye shoonya bhinnata asate (sthirank asato), tevha kshullak prakaran vagalata, asambandhit yadruchchik chalanmadhye, shoonyacha, nashpati sahsambandh gunank asato. yaa prakaranat parasparsambandh anirdharit aahe.
sarvasadharanpane, done yadruchchik chalanpaiki kiman ekache apekshit moolya 0 asel asha vishesh prakaranavyatirikt, parasparsambandhitata hii orthogonalitisarkhi nasate. yaa prakaranat, sahsambandh hii utpadanachi apeksha asate aanee sootra _ 1 aanee sootra _ 2 heey jarr aanee sootra _ 6 asel tarach parasparsambandhit nasatat.
jarr sootra _ 1 aanee sootra _ 2 heey maryadit maryadit kshanansah swatantra asateel, tarr teey parasparsambandhit naheet. tathapi, serve asambandhit chull swatantra nasatat.
vyakhya.
done vastavik yadruchchik chalanchi vyakhya.
jarr tyanche sahparivartan sootra _ 10 shoonya asel tarr done yadruchchik chull sootra _ 9 laa asambandhit mhanatat. aupcharikpaneh
done jatil yadruchchik chalanchi vyakhya.
jarr tyanche sahprasaran sootra _ 12 aanee tyanche chhadm-sahprasaran sootra _ 13 shoonya asel tarr done jatil yadruchchik chull sootra _ 11 laa asambandhit mhanatat.eae.
sootra _ 14
donpeksha jaast yadruchchik chalanchi vyakhya.
done kinwa adhik yadruchchik chull sutranchya _ 15 chya sanchala jarr tyanchi pratyek jodee parasparsambandhit nasel tarr tyala parasparsambandhit mhatale jaate. yadruchchik vector sootra _ 17 chya autocovarians matricks sootra _ 16 chey karn nasalelya ghatak serve shoonya aahet yaa garajechya samatulya aahe. autocovarians matrixchi vyakhya ashee kelee jaateh
parasparsambandhashivay avalambitvachi udaharane.
udaharan 1.
dawa assa aahe qee sootra _ 22 aanee sootra _ 1 madhye shoonya sahparivartan aahe (aanee tyamule teey parasparsambandhit naheet), parantu swatantra naheet.
puravah
heey lakshat gheuun
jethe sootra _ 1 aanee sootra _ 2 swatantra asalyamule dusari samanata asate, tithe eka milate
mhanoon, sootra _ 22 aanee sootra _ 1 heey parasparsambandhit naheet.
sootra _ 22 aanee sootra _ 1 chya swatantryacha arth assa aahe qee serve sootra _ 34 aanee sootra _ 35, sootra _ 36 sathee. heey kharey nahee, visheshtah sootra _ 37 aanee sootra _ 38 sathee.
tyamule sootra _ 41 mhanje sootra _ 22 aanee sootra _ 1 swatantra naheet.
kyu.eae.dii.
udaharan 2.
jarr sootra _ 1 heey sootra _ 45 aanee sootra _ 46 varr eksamanpane vitarit kelele satat yadruchchik chull asel, tarr sootra _ 1 sootra _ 2 nirdharit karat asale taree sootra _ 1 aanee sootra _ 2 parasparsambandhit naheet aanee sootra _ 2 chey vishisht moolya sootra _ 1 chya keval eka kinwa done mulyandware tayar kele jaau shakateh
sootra _ 53
dusarikade, sootra _ 55 dware paribhashit kelelya trikonavar sootra _ 54 heey 0 aahe, jaree sootra _ 56 yaa kshetravar shoonya nahee. 
mhanoon sootra _ 57 aanee chull swatantra naheet.
sootra _ 58
kuthe?
aanee
asambandhit yadruchchik prakriya.
jarr tyanche paraspar sahsambandh sootra _ 63 sarvkal shoonya asel tarr _ 61 aanee _ 62 yaa done yadruchchik prakriyanna asambandhit mhanatat. aupcharikpaneh

