Аналитическая геометрия. Шурыгин В.В. - 41 стр.

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(x
i
M
) {O
0
, e
0
i
}
Φ : E
n
→ E
0
n
n 3
R
3
m π
m
E
n
m
V
n
g : V
n
×V
n
→ R
e
i
V
n
g(a, b) = δ
ij
a
i
b
j
= a
1
b
1
+a
2
b
2
+. . .+a
n
b
n
V
n
A
n
A
n
A
2
ABCD
AB CD
AC BD
AB CD
O AB E CD
A
2
−−→
OB
−−→
OE
A
2
E
2
ABCD
OE
(xiM ) -8,-/08*7?,- 3*.*36 {O , e } \ 9b79*8/9 0[-;-3O0[;-; *b170L-bN
                                         0   0
6OO0,,N .3-/836,/8b Φ : E → E =                i

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


/8b2*8 8-7?1- -L,- *b170L-b- 6OO0,,-* .3-/836,/8b- L6,,-M 36[;*3,-K
/80 n = { )6/8,-/80\ b/* *b170L-b 6OO0,,* .3-/836,/8b6 36[;*3,-/80 3
0[-;-3O, :*-;*830)*/1-;2 .3-/836,/8b2 0 *b170L-b2 6OO0,,-;2 .3-K
/836,/8b2 R =
    ˆ)*b0L,-\ b/9169 mK.7-/1-/8? π b E 9b79*8/9 mK;*3,; *b170L-b;
                     3



6OO0,,; .3-/836,/8b-;=                              m   n


    ð͵xñÍXWxZ €6 b/91-; b*18-3,-; .3-/836,/8b* V \ [6L6b .3-0[b-7?,;
-+36[-; /0;;*830),2J .-7-|08*7?,- -.3*L*7*,,2J +070,*M,2J O-3;2             n


g : V ×V → R \ ;-|,- bb*/80 /83218232 *b170L-b6 b*18-3,-:- .3-/836,K
/8b6= “8- ;-|,- -/2}*/8b08?\ ,6.30;*3\ /7*L2J}0; -+36[-;† b+36b .3-K
         n       n


0[b-7?,M +6[0/ e b V \ .-7-|08? g(a, b) = δ a b = a b +a b +. . .+a b =
(16[6,,; /.-/-+-; ;-|,- bb*/80 861|* ,-b-* /16793,-* .3-0[b*L*,0* b
                                                                      i j       1 1   2 2   n n
                         i       n                               ij


*b170L-b-; b*18-3,-; .3-/836,/8b* ‚b 1-8-3-; -L,- /16793,-* .3-0[b*L*K
,0* 2|* */8?ƒ= ¼/70 bb*/80 /83218232 *b170L-b6 .3-/836,/8b6 ,6 b*18-3K
,-; .3-/836,/8b* V \ 6//- 003-b6,,-; / 6OO0,,; .3-/836,/8b-; A \
8- 8*; /6;; ,6 .3-/836,/8b* A +2L*8 bb*L*,6 /83218236 *b170L-b6 6OK
                             n                                                                n


O0,,-:- .3-/836,/8b6=                        n

    {b*L*,0* /8321823 *b170L-b6 .3-/836,/8b6 b 6OO0,,-; .3-/836,/8K
b* ;-|*8 +8? 0/.-7?[-b6,- .30 3*I*,00 1-,13*8,N [6L6)= H30;*3-;
;-|*8 /72|08? /7*L2J}69 [6L6)6=
    ðÍwÍñÍ rZ €6 6OO0,,-M .7-/1-/80 A L6,6 836.* 09 ABCD / .6367K
7*7?,;0 /8-3-,6;0 AB 0 CD = ‡-16[68?\ )8- 8-)16 .*3*/*)*,09 L06:-K
                                                             2


,67*M AC 0 BD 7*|08 ,6 .39;-M\ .3-N-L9}*M )*3*[ /*3*L0, -/,-b6,0M
AB 0 CD =
    àxÿxXWxZ H2/8? O · /*3*L0,6 AB \ 6 E · /*3*L0,6 CD ‚/;= 30/= ]ãƒ= {b*K
L*; ,6 A /16793,-* .3-0[b*L*,0*\ .- -8,-I*,0J 1 1-8-3-;2 −OB −→ 0 −−→
                                                                   OE ·
       )                                     ­
*L0,0 ,* b[60;,- -38-:-,67?,* b*18-3= ,6+|*,,69 ~80; /16793,;
             2


.3-0[b*L*,0*;\ A .3*b36}6*8/9 b *b170L-b2 .7-/1-/8? E \ ,6 1-8-3-M
836.* 09 ABCD 9b79*8/9 36b,-+-),-M 0\ /7*L-b68*7?,-\ /0;;*830),-M
                         2                                                            2


-8,-/08*7?,- .39;-M OE =
                                     ¸Ü

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