Аналитическая геометрия. Часть III. Многомерные пространства. Гиперповерхности второго порядка. Шурыгин В.В. - 92 стр.

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[ϕ](Φ) = Ψ P
n
ϕ(
e
Φ) =
e
Ψ V
n+1
P
n
A
n+1
V
n+1
P
n
p
X
α=1
(x
α
)
2
−
p+q
X
α=p+1
(x
α
)
2
= 0, 1 6 p + q 6 n + 1, p > q.
P
2
P
2
1
◦
. (x
1
)
2
+ (x
2
)
2
+ (x
3
)
2
= 0 ( )
2
◦
. (x
1
)
2
+ (x
2
)
2
− (x
3
)
2
= 0 ( )
3
◦
. (x
1
)
2
+ (x
2
)
2
= 0 ( )
4
◦
. (x
1
)
2
−(x
2
)
2
= 0 ( )
5
◦
. (x
1
)
2
= 0 ( )
2
◦
A
2
=
P
2
\ P
1
P
1
x
3
= 0 x
2
= 0 x
2
+ x
3
= 0
2
◦
x
3
x
2
X
1
= x
1
/x
3
, X
2
=
x
2
/x
3
X
1
= x
3
/x
2
, X
2
= x
1
/x
2
(X
1
)
2
+ (X
2
)
2
= 1 (X
1
)
2
− (X
2
)
2
= 1
y
1
= x
1
y
2
= x
2
−x
3
y
3
= x
2
+ x
3
(y
1
)
2
+ y
2
y
3
= 0
P
1
y
3
= 0 y
3
X
1
= y
1
/y
3
, X
2
= y
2
/y
3
(X
1
)
2
+ X
2
= 0
P
3
P
3
’-/1-6>12 [ϕ](Φ) = Ψ B Pn 7-9D5 0 7-6>1- 7-9D5 1-9D5 ϕ(Φ)
                                                        e =Ψ e B Vn+1 
7- 165//0„015½08 90.*3.-B*3C,-/7*” B .3-*170B,-: .3-/735,/7B* Pn ¨1
B0B56*,7,5 165//0„015½00 1-,2/-B B An+1 0 ¨1B0B56*,7,5 165//0„015½00
1B5D3570),AC „-3: B 5//-½003-B5,,-: B*17-3,-: .3-/735,/7B* Vn+1 < ’-
¨7-:2 B/8158 90.*3.-B*3C,-/7> B7-3-9- .-38D15 B Pn B .3-*170B,AC 1--3
D0,575C :-“*7 +A7> E5D5,5 -D,0: 0 7-6>1- -D,0: 0E 235B,*,0” B0D5
                                                                           •»º‹
           p
           X              p+q
                          X
                  α 2
                 (x ) −         (xα )2 = 0,   1 6 p + q 6 n + 1, p > q.

      65//0„015½08 130BAC B7-3-9- .-38D15 B P2 <
           α=1            α=p+1


     Y—XYœ^  km vfakcm kigfgxg egftnvj k P2 efgmviakbg zvkakjombibc
igxnj a igo‚vg igxnjw vgxnj k bmvgigfcr efgmviakbcr hahimdjr vggf p
nabji gba ljnj{iht gnbad a imd ym }fjkbmbamd al homn}{qmxg heahvj
                                                 u
    1◦ . (x1 )2 + (x2 )2 + (x3 )2 = 0 ( dbadc gkjo) 
                                                       u
    2◦ . (x1 )2 + (x2 )2 − (x3 )2 = 0 ( kmqmhikmbbc gkjo) 
                                                      v
    3◦ . (x1 )2 + (x2 )2 = 0 ( ejfj dbadcr emfmhm j{qarht eftdcr ) 
                                                             v
    4◦ . (x1 )2 − (x2 )2 = 0 ( ejfj kmqmhikmbbcr emfmhm j{qarht eftdcr ) 
                                      n
    5◦ . (x1 )2 = 0 ( ejfj hgkej j{qar eftdcr ) €
    ªœZœ«œ µÛ^ ’-15“07*  )7- -935,0)*,08 B*ˆ*/7B*,,-9- -B565 2◦ ,5 A =
P2 \ P1 D68      .38:AC          0:*‡ˆ0C                           0
                                         235B,*,08 x3 = 0  x2 = 0 x2 + x3 = 0 
                                                                               2
                            P1 
.3*D/75B68‡7 /-+-” ¨660./  90.*3+-62 0 .535+-62 /--7B*7/7B*,,- <
    ÈYÉY\]Y^ .*3BAC DB2C /62)58C ,2“,- .-D*607> 235B,*,0* 2◦  /--7B*7
/7B*,,-  ,5 x3 0 x2  .-/6* )*9- B 5„„0,,AC 1--3D0,575C X 1 = x1/x3, X 2 =
                                               )
x2 /x3 0 X 1 = x3 /x2 , X 2 = x1 /x2 .-62 5*:  /--7B*7/7B*,,-  235B,*,08
                                                               )
(X 1 )2 + (X 2 )2 = 1 0 (X 1 )2 − (X 2 )2 = 1 < 73*7>*: /62 5* ,2“,- /,5 565
                                                                             )
-/2ˆ*/7B07> .3*-+35E-B5,0* 1--3D0,57 y1 = x1  y2 = x2 − x3  y3 = x2 + x3 <
   ,-B-” /0/7*:* 1--3D0,57 -B56 0:**7 235B,*,0* (y1)2 + y2y3 = 0  5 .38
:58 P1 F 235B,*,0* y3 = 0 < ’-D*60B ,5 y3  B 5„„0,,AC 1--3D0,575C
                                    )
X 1 = y 1 /y 3 , X 2 = y 2 /y 3 .-62 5*: 235B,*,0* .535+-6A (X 1 )2 + X 2 = 0 <
    á[œ˜˜]]™œâ]® W—›YX×\—˜šY° ›š—X—Ú— W—X®Z™œ › P3 ^
     Y—XYœ^  km vfakcm kigfgxg egftnvj k P3 efgmviakbg zvkakjombibc
igxnj a igo‚vg igxnjw vgxnj k bmvgigfcr efgmviakbcr hahimdjr vggf p
nabji gba ljnj{iht gnbad a imd ym }fjkbmbamd al homn}{qmxg heahvj
                                           Ñ

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