Аналитическая геометрия. Часть III. Многомерные пространства. Гиперповерхности второго порядка. Шурыгин В.В. - 79 стр.

UptoLike

Составители: 

a b P
n
A
n
P
n
= A
n
P
n1
(π)
v
V
2
(a) V
2
(b) = L(v)
p(v) P
n1
(π)
P
n
A
i
i = 1, 2, . . .
A
A
i
A A A
n
k i > k A
i
A
n
lim
i→∞
A
i
= A
A
i
i = 1, 2, . . . ` v
A
n
p(v) P
n1
(π)
P
n
A P
n
a
V
n+1
P
n
p(a) = A
A = [a] [a] = [b] b =
λa {e
α
} α = 1, . . . , n + 1 V
n+1
a = a
α
e
α
A a
α
α = 1, . . . , n + 1
a
α
b
α
P
n
b
α
= λa
α
α = 1, . . . , n + 1
/73032*7/8 .*3*/*)*,0*: DB2C +-6>‰0C
-132“,-/7*” /„*3A B DB2C D05:*7356>
,- .3-70B-.-6-“,AC 7-)15C <
      5//:-730: DB* .38:A* a 0 b B Pn 
.*3*/*)*,0* 1-7-3AC / An 0E 5„„0,,-”
:-D*60 •I»‹ Pn = An ∪ Pn−1(π) .3*D/75B
68*7 /-+-” .53566*6>,A* 5„„0,,A* .38
:A* / ,5.35B68‡ˆ0: B*17-3-: v < 51 151
V2 (a) ∩ V2 (b) = L(v)  7- ¨70 .38:A* .*
3*/*15‡7/8 B +*/1-,*),- 2D56*,,-” 7-)1*
p(v) ∈ Pn−1 (π) <
    ªœY«œ\]Y^ .3-*170B,-: .3-/735,/7B* P ,5D .-6*: B*ˆ*/7B*,,AC
)0/*6 :-“,- BB*/70 751-* .-,870* :57*:570)*/1-9-n
                                                      5,560E5 •7-),**  7-
.-6-900‹ 151 .3*D*6 .-/6*D-B57*6>,-/70 7-)*1 Ai  i = 1, 2, . . . < ³7- :-“,-
/D*657>  ,5.30:*3  /6*D2‡ˆ0: -+35E-:~ 7-)15 A 8B68*7/8 .3*D*6-: .-/6*
D-B57*6>,-/70 Ai  */60 B ,*1-7-3-” 5„„0,,-” 1537*  D68 1-7-3-” 7-)15
                           )                          )
A ,* 8B68*7/8 +*/1-,* ,- 2D56*,,-”  7- */7> 751-”  7- A ∈ An  ,5”D*7
/8 751-* ,572356>,-* )0/6- k  )7- .30 i > k B/* 7-)10 Ai .30,5D6*“57
An 0 lim Ai = A < ’30 ¨7-: B/8158 .38:58 .3-*170B,-9- .3-/735,/7B5
-15EAB5*7/8
        i→∞
                 E5:1,27-” 130B-” •7-.-6-90)*/10 ¨1B0B56*,7,-” -132“,-
/70‹< ’3*D*6-: /73*:8ˆ*”/8 1 +*/1-,*),-/70 .-/6*D-B57*6>,-/70 7-)*1
                                                         „„
Ai  i = 1, 2, . . . .38:-” ` / ,5.35B68‡ˆ0: B*17-3-: v 5 0,,-9- .3-/7
35,/7B5 0E 5„„0,,-” :-D*60 •I»‹ 8B68*7/8 7-)15
         An                                               p(v) ∈ Pn−1 (π)<
Ý^Ù VZ\—X—Z\Y ™——XZ]\œš › Pn ^
 -)15 A ∈ Pn -D,-E,5),- -.3*D*68*7/8 6‡+A: B*17-3-: a 0E B*17-3,-9-
.3-/735,/7B5 Vn+1  5//-½003-B5,,-9- / Pn  7510: )7- p(a) = A < ì2D*:
0/.-6>E-B57> /6*D2‡ˆ** -+-E,5)*,0*~ A = [a] < ’30 ¨7-: [a] = [b] ⇔ b =
                                                                              )
λa < ’2/7> {eα }  α = 1, . . . , n + 1  F +5E0/ B Vn+1 0 a = aα eα < -9D5 7- 15
          )                                 )
A -D,-E,5 ,- -.3*D*68*7/8 ,5+-3-: 0/*6 aα  α = 1, . . . , n + 1 < B5 ,5+-35
                                      )
aα 0 bα E5D5‡7 -D,2 0 72 “* 7- 12 .3-/735,/7B5 Pn 7-9D5 0 7-6>1- 7-9D5 
1-9D5 bα = λaα  α = 1, . . . , n + 1 <

                                       ÎÏ