upkshetra qamee karane

rekheey bijganitemadhye, hilbert space sootra _ 3 pasoon swatakade asalelya rekheey nakash sootra _ 2 chey qamee karnare upasthan sootra _ 1 heey sootra _ 4 chey aparivartaniy upasthan aahe jyache orthogonal purak sootra _ 5 heey sootra _ 6 chey aparivartaniy upasthan dekhil aahe, mhanje sootra _ 7 aanee sootra _ 8 asey mhanatat qee upasthan sootra _ 1 heey nakasha sootra _ 6 qamee karate.
eka mhanato qee resheey nakasha qamee karata yenyajoga asel, jarr tyat qamee naan karata yenari upasthan asel. anyatha teey irreducible aahe asey mhanatat.
jarr sootra _ 3 heey maryadit pariman sootra _ 12 chey asel aanee sootra _ 1 heey matricks sootra _ 16 dware aadhar sootra _ 15 antargat darshavilele nakash sootra _ 2 chey qamee karnare upkshetra asel tarr sootra _ 17 hii berries mhanoon vyakt kelee jaau shakate.
sootra _ 18
jethe sootra _ 19 heey sootra _ 3 teey sootra _ 1 paryantchya orthogonal projection matricks aahe aanee sootra _ 22 heey sootra _ 23 vareel projection matricks aahe (yethe sootra _ 24 heey olakh matricks aahe.)
yavyatirikt, sootra _ 3 madhye _ 26 heey orthonormal besis sootra aahe, jeey sootra _ 1 chaa orthonormal aadhar aahe. jarr sootra _ 28 heey sootra _ 15 pasoon sootra _ 26 paryantche sankraman matricks asel tarr sootra _ 26 chya sandarbhat sootra _ 4 darshavinare matricks sootra _ 32 heey eka block-diagonal matricks aahe.
sootra _ 34
sootra _ 35 saha jethe sootra _ 36, aanee sootra _ 37

