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16η διάλεξη Γραμμικής Άλγεβρας
- 1. Jemelei¸deic Q¸roi DianusmatikoÐ Q¸roi kai Upìqwroi Grammik 'Algebra DianusmatikoÐ q¸roi kai upìqwroi Tm ma Hlektrolìgwn Mhqanik¸n kai Mhqanik¸n Upologist¸n Panepist mio JessalÐac 30 OktwbrÐou 2014
- 2. Jemelei¸deic Q¸roi DianusmatikoÐ Q¸roi kai Upìqwroi 1h Exètash Proìdou Ï H 1h exètash proìdou ja pragmatopoihjeÐ 9-10 to Sˆbbato 1/11.
- 3. Jemelei¸deic Q¸roi DianusmatikoÐ Q¸roi kai Upìqwroi 1h Exètash Proìdou Ï H 1h exètash proìdou ja pragmatopoihjeÐ 9-10 to Sˆbbato 1/11. Ï Aforˆ mìnon touc/tic prwtoeteÐc kai eÐnai upoqrewtik .
- 4. Jemelei¸deic Q¸roi DianusmatikoÐ Q¸roi kai Upìqwroi 1h Exètash Proìdou Ï H 1h exètash proìdou ja pragmatopoihjeÐ 9-10 to Sˆbbato 1/11. Ï Aforˆ mìnon touc/tic prwtoeteÐc kai eÐnai upoqrewtik . Ï Exetastèa Ôlh eÐnai h didaqjeÐsa mèqri kai thn Paraskeu 24/10.
- 5. Jemelei¸deic Q¸roi DianusmatikoÐ Q¸roi kai Upìqwroi 1h Exètash Proìdou Ï H 1h exètash proìdou ja pragmatopoihjeÐ 9-10 to Sˆbbato 1/11. Ï Aforˆ mìnon touc/tic prwtoeteÐc kai eÐnai upoqrewtik . Ï Exetastèa Ôlh eÐnai h didaqjeÐsa mèqri kai thn Paraskeu 24/10. Ï H exètash ja xekin sei akrib¸c stic 9.
- 6. Jemelei¸deic Q¸roi DianusmatikoÐ Q¸roi kai Upìqwroi 1h Exètash Proìdou Ï H 1h exètash proìdou ja pragmatopoihjeÐ 9-10 to Sˆbbato 1/11. Ï Aforˆ mìnon touc/tic prwtoeteÐc kai eÐnai upoqrewtik . Ï Exetastèa Ôlh eÐnai h didaqjeÐsa mèqri kai thn Paraskeu 24/10. Ï H exètash ja xekin sei akrib¸c stic 9. Ï Perissìterec plhroforÐec sthn erqìmenh diˆlexh thc Paraskeu c.
- 7. Jemelei¸deic Q¸roi DianusmatikoÐ Q¸roi kai Upìqwroi Erwt mata Ï EÐnai ta dianÔsmata tou x°²º¶·´ ìla lÔseic tou sust matoc? Ï EÐnai ta dianÔsmata tou x°²º¶·´ ìlec oi lÔseic tou sust matoc? Ï Upˆrqei kai ˆlloc trìpoc anaparˆstashc tou x°²º¶·´? Ï Kˆtw apo poièc sunj kec èna sÔsthma èqei lÔsh?
- 8. Jemelei¸deic Q¸roi DianusmatikoÐ Q¸roi kai Upìqwroi 'Uparxh lÔsewn Ï An èna omogenèc sÔsthma Ax Æ 0 èqei perissìterouc agn¸stouc apo exis¸seic (n Èm) tìte èqei mia toulˆqiston mh-terimènh lÔsh.
- 9. Jemelei¸deic Q¸roi DianusmatikoÐ Q¸roi kai Upìqwroi 'Uparxh lÔsewn Ï An èna omogenèc sÔsthma Ax Æ 0 èqei perissìterouc agn¸stouc apo exis¸seic (n Èm) tìte èqei mia toulˆqiston mh-terimènh lÔsh. Ï To sÔnolo twn mh-tetrimènwn lÔsewn tou omogenoÔc sust matoc Ax Æ 0 eÐnai Ðso me to sÔnolo twn mh-tetrimènwn lÔsewn tou omogenoÔc sust matoc Ux Æ 0 ìpou U o ˆnw klimakwtìc pÐnakac pou prokÔptei apo ton A me apaloif .
- 10. Jemelei¸deic Q¸roi DianusmatikoÐ Q¸roi kai Upìqwroi 'Uparxh lÔsewn 'Estw ìti h apaloif metatrèpei to sÔsthma Ax Æ b sto sÔsthma Ux Æ c. 'Estw epÐshc ìti upˆrqoun r (mh-mhdenikoÐ) odhgoÐ tìte Ï r Æ min{m,n}.
- 11. Jemelei¸deic Q¸roi DianusmatikoÐ Q¸roi kai Upìqwroi 'Uparxh lÔsewn 'Estw ìti h apaloif metatrèpei to sÔsthma Ax Æ b sto sÔsthma Ux Æ c. 'Estw epÐshc ìti upˆrqoun r (mh-mhdenikoÐ) odhgoÐ tìte Ï r Æ min{m,n}. Ï Oi teleutaÐec m¡r grammèc tou U eÐnai mhdenikèc.
- 12. Jemelei¸deic Q¸roi DianusmatikoÐ Q¸roi kai Upìqwroi 'Uparxh lÔsewn 'Estw ìti h apaloif metatrèpei to sÔsthma Ax Æ b sto sÔsthma Ux Æ c. 'Estw epÐshc ìti upˆrqoun r (mh-mhdenikoÐ) odhgoÐ tìte Ï r Æ min{m,n}. Ï Oi teleutaÐec m¡r grammèc tou U eÐnai mhdenikèc. Ï An r Æm upˆrqei pˆnta lÔsh
- 13. Jemelei¸deic Q¸roi DianusmatikoÐ Q¸roi kai Upìqwroi 'Uparxh lÔsewn 'Estw ìti h apaloif metatrèpei to sÔsthma Ax Æ b sto sÔsthma Ux Æ c. 'Estw epÐshc ìti upˆrqoun r (mh-mhdenikoÐ) odhgoÐ tìte Ï r Æ min{m,n}. Ï Oi teleutaÐec m¡r grammèc tou U eÐnai mhdenikèc. Ï An r Æm upˆrqei pˆnta lÔsh Ï Upˆrqei lÔsh tou omogenoÔc mìnon an oi teleutaÐec m¡r sunÐst¸sec tou c eÐnai kai autèc mhdenikèc.
- 14. Jemelei¸deic Q¸roi DianusmatikoÐ Q¸roi kai Upìqwroi 'Uparxh lÔsewn 'Estw ìti h apaloif metatrèpei to sÔsthma Ax Æ b sto sÔsthma Ux Æ c. 'Estw epÐshc ìti upˆrqoun r (mh-mhdenikoÐ) odhgoÐ tìte Ï r Æ min{m,n}. Ï Oi teleutaÐec m¡r grammèc tou U eÐnai mhdenikèc. Ï An r Æm upˆrqei pˆnta lÔsh Ï Upˆrqei lÔsh tou omogenoÔc mìnon an oi teleutaÐec m¡r sunÐst¸sec tou c eÐnai kai autèc mhdenikèc. Ï An r Æ n to omogenèc sÔsthma èqei mìnon thn tetrimènh lÔsh
- 15. Jemelei¸deic Q¸roi DianusmatikoÐ Q¸roi kai Upìqwroi Tèssera shmantikˆ sÔnola Ï Mhdenìqwroc N (A) Ï Q¸roc Sthl¸n R(A) Ï Q¸roc Gramm¸n R ¡ AT¢ Ï Aristerìc Mhdenìqwroc N ¡ AT¢