Аналитическая геометрия. Шурыгин В.В. - 26 стр.

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A
n
{O, e
i
} O ∈ A
n
{e
i
} i = 1, . . . , n V
n
A {O, e
i
}
r
A
=
−→
OA
(A, V, ψ) (A
0
, V
0
, ψ
0
)
Φ : A → A
0
Φ
ϕ : V → V
0
ϕ(
−→
AB) =
−−→
A
0
B
0
A
0
= Φ(A), B
0
= Φ(B).
Φ : A → A
0
A A
0
Φ : A → A
0
ϕ : V → V
0
Φ
A
0
= Φ(A) B
0
= Φ(B) C
0
= Φ(C) D
0
= Φ(D)
−→
AB =
−−→
CD =⇒
−−→
A
0
B
0
=
−−→
C
0
D
0
.
Φ : A → A
0
ϕ : V → V
0
A
n
A
0
n
{O, e
i
} A
n
{O
0
, e
0
i
}
A
0
n
Φ M ∈
A
n
(x
i
M
) {O, e
i
} M
0
∈
A
0
n
(x
i
M
) {O
0
, e
0
i
}
Φ : A
n
→ A
0
n
n
     Ž¡ŽŠ’ b 6OO0,,-; .3-/836,/8b* A ‚161 0 b :*-;*830)*/1-; .3-K
/836,/8b*ƒ ,6[b6*8/9 ,6+-3 {O, e } \ /-/8-9}0M 0[ 8-)10 O ∈ A 0 +6K
                                                              n


[0/6 {e } \ i = 1, . . . , n \ 6//- 003-b6,,-:- b*18-3,-:- .3-/836,/8b6 V =
                                              i                                                           n


  ªŒœº”Ž‰žŠŠ’ 8-)10 A -8,-/08*7?,- 3*.*36 {O, e } ,6[b6*8/9 b*18-3
          i                                                                                                                   n

                                     )           )
r = OA = „61 |*\ 161 0 b /72 6* :*-;*830 */1-:- .3-/836,/8b6\ 0;*J8
       −→
                                                                                              i


;*/8- O-3;27 ‚•]ƒ=
 A


   ϳTxwx™xXWxZ ›œžŸ (A, V, ψ) Œ (A , V , ψ ) ª” ÉɌ‘Ð ¡Šžº
ž”§ 袏Œ’ŠŠªŠ¢¤ŠŽ ŠžŠ¬»ŽŒŽ Φ : A → A ¢‘”Žž£ Œ¢Š’Š º
                                                          0   0           0



Ɍ¢’Š’ ÉɌ‘Ð ¡Šžž”¥ Ž‹Œ Φ ŒªœÑŒœŽž Œ¢Š’ŠÉŒ¢’ ŠÑŒº
                                                                                          0



ŒŠ”‘Ð ”Ž‰žŠ‘Ð ¡Šžž”¥ žŠ ŽžŸ Ž‹Œ œ«Žž”œŽž Œ¢Š’Š º
Ɍ¢’ ϕ : V → V ž‰Š¦¥ ¤žŠ
                  0

                    −→
                ϕ(AB) = A B   0
                                −−→
                                  0               0
                                        A = Φ(A), B = Φ(B).             ‚•Úƒ  0

ޝ‹Œ œ«Žž”œŽž Œ¢Š’ŠÉŒ¢’ Φ : A → A ¥ žŠ ÉɌ‘Ž ¡Šžž”   0

A Œ A ¢‘”Àž£ Œ¢Š’ŠÉ‘’Œ§
      0
   ¼/70 Φ : A → A · 0[-;-3O0[; 6OO0,,N .3-/836,/8b\8- 0[-;-3O0[;
                      0
b*18-3,N .3-/836,/8b ϕ : V → V \ -.3*L*79*;M /--8,-I*,0*; ‚•Úƒ\
                                                      0
,6[b6*8/9 0[-;-3O0[;-;\ ŠÑŒŒŠ”‘’ / 0[-;-3O0[;-; Φ =
   ­7*L2*8 -8;*808?\ )8- 0[ 2/7-b09 ‚•Úƒ .3*|L* b/*:- /7*L2*8\ )8- */70
A = Φ(A) \ B = Φ(B) \ C = Φ(C) \ D = Φ(D) \ 8-
 0            0           0                       0

                        −→ −−→              −−→ −−→
                        AB = CD =⇒ A B = C D .                0       0 ‚•òƒ      0   0


„-7?1- .30 b.-7,*,00 2/7-b09 ‚•òƒ -8-+36|*,0* Φ : A → A 0,L2 032*8                                   0
,*1-8-3-* -8-+36|*,0* ϕ : V → V =         0
   ˜Txw™ušxXWxZ ôÀ¬‘Ž ª” ÉɌ‘Ž ¡Šžž” ŠªŠ¦ ¢’ŽŠžŒ
A Œ A Œ¢Š’ŠÉ‘§
          0
 n
   éuyÍêÍzx™ë¶ztuZ H2/8? {O, e } · .3-0[b-7?,M 3*.*3 b A \ 6 {O , e }
          n



· .3-0[b-7?,M 3*.*3 b A \ 8-:L6 -8-+36|*,0* Φ \ -8,-/9}** 8-))1* M ∈
                                                                                                                  0       0
                                      i                                                               n                       i
                              0

A \ 0;*J}*M 1--3L0,68 (x ) -8,-/08*7?,- 3*.*36 {O, e } \ 8- 12 M ∈
                              n
                                  i                                                                                   0

A \ 0;*J}2J 8* |* /6;* 1--3L0,68 (x ) -8,-/08*7?,- 3*.*36 {O , e } \
 n                                M                                                               i
 0                                                            i                                               0       0
9b79*8/9 0[-;-3O0[;-; Φ : A → A = 
 n
                                                  0
                                                              M                                                           i


   —[ ~8-:- .3*L7-|*,09 /7*L2*8\ )8-\ / 8-),-/8?J L- 0[-;-3O0[;6\ /2K
                                  n               n


}*/8b2*8 8-7?1- -L,- 6OO0,,-* .3-/836,/8b- L6,,-M 36[;*3,-/80 n = {
                                         ïÁ

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