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Διάλεξη 27η - Προβολές και ελάχιστα τετράγωνα

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Text of Διάλεξη 27η - Προβολές και ελάχιστα τετράγωνα

  • 1. GRAMMIKH ALGEBRA 27h dilexh:Probolc23 Noembrou 2012

2. Probol se eujea tou R nNa breje h probol p tou b epnw sthn eujeapou orzei to aNa breje to plhsistero stob shmeo p thceujeac pou orzei to aTo a dirqetai apo thn arq twn axnwn. 3. Probol se eujea tou R n 4. Probol se eujea tou R n 5. H probolp enc dianmatocb Rnse mia eujea a Rn poupernei apo to0 6. Hprobol p enc dianmatocb Rn se mia eujeaa Rn pouperneiapo to 0T - enai h p = aT b a a a 7. Hprobol p enc dianmatocb Rn semia eujea a Rn pouperneiapo to 0T - enai h p = aT b a a a - me antstoiqo pnaka probolc aaT P = aT a 8. Hprobolp encdianmatocb Rnsemia eujea a Rn pouperneiapo to0 T - enaih p = aT b aa a - me antstoiqopnaka probolc aa T P = aT a 1 9. Pardeigma1 1 - Probol tou 2 sto 13 1 10. Pardeigma1 1 - Probol tou 2 sto 13 11 - Pnakac probolc sto 11 11. Pardeigma1 1 - Probol tou 2 sto 13 11 - Pnakac probolc sto 1 kai1 cos sto sin 12. Efarmog 13. EfarmogUpologste x ttoio ste Ax = b 14. EfarmogUpologste x ttoio ste Ax = b kai x R(A)./ 15. EfarmogUpologste x ttoio ste Ax = b kai x R(A)./ 16. Elqista TetrgwnaAn Ax = b kai x R(A)/tte 17. Elqista TetrgwnaAn Ax = b kai x R(A)/ttemiaprosggish thclshc xenai hlsh y tou sustmatoc Ay = ppou p h probol toubstonR(A). 18. Elqista Tetrgwna Ax = b 19. Elqista Tetrgwna Ax = b AT Ax = AT b 20. Elqista Tetrgwna Ax = b AT Ax = AT b x = AT AAT b 1 21. Elqista TetrgwnaAx = b AT Ax = AT b x = AT AAT b1Prgmati AT (Ax b) = 0 22. Elqista TetrgwnaAx = b AT Ax = AT b x = AT A AT b 1Prgmati AT (Ax b) = 0Upjesh: oi stlec touAenai 23. Pardeigma 1 44 1 5 x = 5 0 66