1. ParagontopoÐhsh LU
Grammik 'Algebra
ParagontopoÐhsh
Tm ma Hlektrolìgwn Mhqanik¸n kai Mhqanik¸n Upologist¸n
Panepist mio JessalÐac
20 OktwbrÐou 2014
2. ParagontopoÐhsh LU
ParagontopoÐhsh AÆ LU
Kˆje tetragwnikìc pÐnakac A mporeÐ na analujeÐ
se ginìmeno enìc kˆtw trigwnikoÔ pÐnaka L me
monˆdec sthn diag¸nio kai enìc ˆnw trigwnikoÔ
pÐnaka U.
Ï O L èqei touc pollaplasiastèc thc apaloif c
kˆtw apo thn diag¸nio
Ï O U ta stoiqeÐa tou A ìpwc autˆ prokÔptoun
metˆ thn apaloif
3. ParagontopoÐhsh LU
'Uparxh kai monadikìthta LU
Je¸rhma
Oi pÐnakec L U pou perigrˆfjhkan parapˆnw
Ï upˆrqoun kai
Ï kai an o A eÐnai antistrèyimoc eÐnai monadikoÐ.
Apìdeixh.
LkLk¡1 ¢ ¢ ¢L3L2L1AÆU!AÆ (L1)¡1 (L2)¡1 (L3)¡1 ¢ ¢ ¢
¡
Lk¡1
¢¡1 ¡
Lk
¢¡1U
L1U1 Æ L2U2!(L2)¡1 L1 ÆU2 (U1)¡1
10. ParagontopoÐhsh LU
EpÐlush Sust matoc me ParagontopoÐhsh AÆ LU
Na lujeÐ to Ax an gnwrÐzoume thn LU
paragontopoÐhsh tou
11. ParagontopoÐhsh LU
EpÐlush Sust matoc me ParagontopoÐhsh AÆ LU
Na lujeÐ to Ax an gnwrÐzoume thn LU
paragontopoÐhsh tou
Ï Ax Æ b)LUx Æ b)L(Ux) Æ b
12. ParagontopoÐhsh LU
EpÐlush Sust matoc me ParagontopoÐhsh AÆ LU
Na lujeÐ to Ax an gnwrÐzoume thn LU
paragontopoÐhsh tou
Ï Ax Æ b)LUx Æ b)L(Ux) Æ b
Ï Jètw y ÆUx kai èqw Ly Æ b
13. ParagontopoÐhsh LU
EpÐlush Sust matoc me ParagontopoÐhsh AÆ LU
Na lujeÐ to Ax an gnwrÐzoume thn LU
paragontopoÐhsh tou
Ï Ax Æ b)LUx Æ b)L(Ux) Æ b
Ï Jètw y ÆUx kai èqw Ly Æ b
Ï LÔnw to Ly Æ b gia na upologÐsw to y
14. ParagontopoÐhsh LU
EpÐlush Sust matoc me ParagontopoÐhsh AÆ LU
Na lujeÐ to Ax an gnwrÐzoume thn LU
paragontopoÐhsh tou
Ï Ax Æ b)LUx Æ b)L(Ux) Æ b
Ï Jètw y ÆUx kai èqw Ly Æ b
Ï LÔnw to Ly Æ b gia na upologÐsw to y
Ï LÔnw to Ux Æ y gia na upologÐsw to x