null vector

ganitat, sambandhit vargakar swaroop 'q' saha vector jaaga 'x' dilee, tarr lihilele, null vector kinwa isotropic vector haah 'x' chaa shoonya nasalela ghatak 'x' aahe.
vastavik dwillingi swarupanchya siddhantat, nishchit dvighat swaroop aanee samasthanik dvighat swaroop vegale aahet. teey keval nantarchya sathee vegale kele jaatat, tethe shunyetar null vector astitvat aahe.
jyaa chaturbhuj jaaget null vector asato tyala syudo-euclidean space mhanatat.
chhadm-euclidean vector jaaga orthogonal upasthananmadhye vighatit (adviteey nasaleli) kelee jaau shakate, jethe "aii" varr "kyu" sakaratmak-nishchit aanee "bii" varr nakaratmak-nishchit aahe. x" chya null coone kinwa isotropic konmadhye santulit golakanche millen asateh
sootra _ 1
null coone haah moodatoon samasthanik reshancha sangam dekhil aahe.
algebra vibhajit qaraa.
null vectors rachana bijganit haah vibhajit bijganit aahe.
rachana bijganitache ("aaa", "+", "×", *), vargakar swaroop q ("x") = "xx" * aahe. jevha "x" haah null vector asato tevha "x" sathee gunakar vyutkram nasato aanee "x" inc ≤ 0 "asalyane, a" haah vibhajanacha bijganit nasato.
callie-dicksonchya bandhkamat, dvi-sankul sankhya, dvi-pratyutar aanee jaiv-pratyutar yaa malikanmadhye vibhajit algebra udbhavtat, jeey jatil sankhya kshetra sootra _ 2 chaa vapar yaa duheri bandhkamacha paya mhanoon karatat. eae. dixon (1919). visheshtah, yaa algebranche done kalpanik ekak asatat, jeey pravas karatat, tyamule tyanche utpadan, jevha varg kele jaate, tevha + 1 milateh
vastavik up-algebra, vibhajit jatil sankhya, vibhajit chaturthansh aanee vibhajit-aktonion, tyanchya null shankunsah 0 ω "a" chya aat aanee baher prakash magova darshavitat, spacetime topology suchavatat.
udaharane.
minkowski jaageche prakashasarkhe vahak null vector aahet.
chaar resheey swatantra dvigunit, aanee shoonya vahak aahet aanee avkashkal darshavinyasathi vaparlya jaanarya upasthanasathi aadhar mhanoon kaam karoo shakatat. spacetime manifoldschya neuman-penrose formalism drushtikonat dekhil null vectorcha vapar keela jaato.
khote bijganitachya verma modulemadhye null vector asatat.

