Аналитическая геометрия. Часть III. Многомерные пространства. Гиперповерхности второго порядка. Шурыгин В.В. - 10 стр.

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x
1
x
2
x
3
x
4
x
5
=
1
0
2
0
1
+ λ
1
1
1
0
0
1
+ λ
2
4
1
1
−2
−1
π ∩ π
0
π
0
{u
1
, u
2
, u
3
}
−2u
1
− 2u
2
− u
3
= 1 π ∩ π
0
π
0
π
m
∩ π
0
k
= ∅
π
m
= {M
0
, L
m
} π
0
k
= {M
0
0
, L
0
k
}
m 6 k
π
m
π
0
k
(π
m
kπ
0
k
) π
m
∩ π
0
k
= ∅ L
m
⊂ L
0
k
π
m
π
0
k
π
m
∩ π
0
k
= ∅
L
0
k
∩ L
m
= {0}
1) π
m
= {M
0
, L
m
}
π
0
k
= {M
0
0
, L
0
k
}
m 6 k π
m
⊂ π
00
k
π
00
k
kπ
0
k
k π
00
k
π
00
k
= {M
0
, L
0
k
}
2) π
m
π
0
k
(k + m) π
1
k+m
= {M
0
, L
0
k
⊕L
m
} π
2
k+m
= {M
0
0
, L
0
k
⊕L
m
}
M
0
0
π
0
k
M
0
π
m
π
00
k
π
2
k+m
M
0
0
π
0
k
π
1
k+m
M
0
π
m
π
m
π
0
k
r
0
0
− r
0
/∈
L
m
⊕L
0
k
dim(L
m
⊕L
0
k
) = m+k 1+m+k 6 n
n − 1
7/‡D5
                                                                  
                      x1            1               1               4
                                                                  
                     x2          0             1             1    
                                                                  
                     x3   =      2     + λ1    0    + λ2     1    
                                                                  
                                                                  
                     x4          0             0            −2    
                      x5            1               1              −1
   ’-/1-6>12 .6-/1-/7> π ∩ π0  35//:5730B5*:58 151 .-D:,-“*/7B- B 5„
„0,,-: .3-/735,/7B* π0 / 1--3D0,575:0 {u1, u2, u3}  E5D5*7/8 -D,0: 235B
,*,0*: −2u1 − 2u2 − u3 = 1  7- π ∩ π0 F 90.*3.6-/1-/7> B π0 <
   µ^ π ∩ π 0 = ∅ <
   VWXYZY[Y\]Y^     ž}hi‚ njbc nkm eoghvghia πm = {M0, Lm} a πk0 = {M00 , L0k }
       m      k


aw not gefmnmombbghiaw m 6 k €
   žoghvghia πm a πk0 bjlckj{iht ejfjoomo‚bcda k hifgxgd hdchom hogp
kj (πmkπk0 ) w mhoa πm ∩ πk0 = ∅ a Lm ⊂ L0k €
   žoghvghia πm a πk0 bjlckj{iht hvfmqakj{qadahtw mhoa πm ∩ πk0 = ∅
a L0k ∩ Lm = {0} €
   :**7 :*/7- /6*D2‡ˆ** -)*B0D,-*
   ŽXYZ[—¡Y\]Y^ 1) Æhoa eoghvghi‚ π = {M , L } ejfjoomo‚bj eoghvgp
hia πk0 = {M00 , L0k } w m 6 k w ig πm ⊂ πk00 w xnm πk00kπk0 € Ðij k peoghvghi‚ πk00
                                          m          0    m


admmi homn}{qau kan πk00 = {M0, L0k } €
                  v                v
   2) Æhoa eogh ghia πm a πk0 h fmqakj{ihtw ig gba omyji k ejfjoomo‚p
bcr (k + m) peoghvghitr πk+m  1
                                  = {M0 , L0k ⊕ Lm } a πk+m  2
                                                                = {M00 , L0k ⊕ Lm } €
                                                                              1
                                πk00                                         πk+m
                           πm                                      πk0
             M0                                         M00


                                                               M0        πm
                   M00                  πk0
                                                                    2
                                                                   πk+m
  E 2/6-B08 •Š¶‹ /6*D2*7 )7- */60 π 0 π0 /13*ˆ0B5‡7/8  7- r0 − r ∈/
Lm ⊕Lk0 < 51 151                     7-
                                      m  k
                 dim(Lm ⊕Lk ) = m+k  1+m+k 6 n <
                          0                       6*D-B57*6>,-
                                                              0
                                                                  /2:
                                                                    0


:5 35E:*3,-/7*” /13*ˆ0B5‡ˆ0C/8 .6-/1-/7*” ,* :-“*7 .3*BA‰57> n − 1 <
                                   Ñ

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