Аналитическая геометрия и линейная алгебра. Умнов А.Е. - 73 стр.

UptoLike

ВУЗ: 

МФТИ | Москва

Составители: 

Рубрика: 

cÈÏ Ëã
77
¯«äÈ«Ò¹ãº°}º°

˺äË¯ÒË°}ºË°ãºmÒË
{ºÏäºÎÓÈ«mË}º¯ÓÈ«Áº¯äÈ¹¯Ë°ÈmãËÓÒ«
ȯÈããËãÓº° ¹ãº°}º°Ë®
rr p q
→→ → →
=+ +
01 1 1
ϕθ
Ò
→→→→
++=
2202
qprr
θϕ
° vË°mË
λ
≠
0
È}ºËº
[,] [,]
pq pq
11 22
→→ →→
=
λ
Ò
(,,)
rrpq
01 02 1 1
0
→→→→
−≠

°
[[ , ],[ , ]]pq pq o
11 2 2
→→ → → →
=
Ò
(,,)rrpq
01 02 1 1
0
→→→→
−≠
vºm¹ÈËÓÒË ¹ãº°}º°Ë®
rr p q
→→ → →
=+ +
01 1 1
ϕθ
Ò
→→→→
++=
2202
qprr
θϕ
° vË°mË
λ
≠
0
È}ºËº
[,] [,]
pq pq
11 22
→→ →→
=
λ
Ò
(,,)
rrpq
01 02 1 1
0
→→→→
−=

°
[[ , ],[ , ]]pq pq o
11 2 2
→→ → → →
=
Ò
(,,)rrpq
01 02 1 1
0
→→→→
−=
|¯ººÓÈãÓº° ¹ãº°}º°Ë®
rr p q
→→ → →
=+ +
01 1 1
ϕθ
Ò
rr p q
→→ → →
=+ +
02 2 2
ϕθ
([ , ],[ , ])
pq pq
11 2 2
0
→→ → →
=

ȯÈããËãÓº° ¹ãº°}º°Ë®
rr p q
→→ → →
=+ +
0
ϕθ
Ò
(,)nr d
→→
=
(,,)
pqn
→→→
=
0
¹¯Ò°ãºmÒÒ
(, )
nr d
→→
≠
0

vºm¹ÈËÓÒË ¹ãº°}º°Ë®
rr p q
→→ → →
=+ +
0
ϕθ
Ò
(,)nr d
→→
=
(,,)pqn
→→→
=
0
¹¯Ò°ãºmÒÒ
(, )nr d
→→
=
0

|¯ººÓÈãÓº° ¹ãº°}º°Ë®
rr p q
→→ → →
=+ +
0
ϕθ
Ò
(,)nr d
→→
=
° vË°mË
λ
≠
0
È}ºËº
[,]pq n
→→ →
=
λ

°
[[,],]
pq n o
→→ → →
=

Òjisq|j|Óº°ÒËãÓÈ«º¯ÒËÓÈÒ«¹ãº°}º°Ë®m¹¯º°¯ÈÓ°mË
c È Ï  Ë ã                                                      77
¯«äȫҹ㺰}º°ˆ 



                                                                                                          
          €Ëºäˈ¯ÒË°}ºË‚°ãºmÒË                                                       {ºÏäºÎÓÈ«mË}ˆº¯ÓÈ«Áº¯äȹ¯Ë°ˆÈmãËÓÒ«
                                                                           
                                                                                                                                                                   → →                    →      →
    È¯ÈããËã Óº°ˆ                            ¹ãº°}º°ˆË® ° v‚Ë°ˆm‚ˈ λ ≠ 0  ˆÈ}ºË ˆº [ p1 , q 1 ] = λ [ p 2 , q 2 ]  Ò
    →        →           →            →                                                   →         →      →       →
        r = r01 + ϕ p1 + θ q1 Ò                                                      (r01 − r02 , p1 , q1 ) ≠ 0 
    →        →           →            →                                     
        r = r02 +ϕ p2 + θ q2                                              
                                                                                          → →               →      →            →             →         →       →      →
                                                                            °[[ p1 , q1 ],[ p2 , q 2 ]] = o Ò ( r01 − r02 , p1 , q1 ) ≠ 0 
                                                                            
                                                                            
                                                                                                                                                                   → →                    →      →
    vºm¹ÈËÓÒË                               ¹ãº°}º°ˆË® ° v‚Ë°ˆm‚ˈ λ ≠ 0  ˆÈ}ºË ˆº [ p1 , q 1 ] = λ [ p 2 , q 2 ]  Ò
    →        →           →            →                                                   →         →      →       →
        r = r01 + ϕ p1 + θ q1 Ò                                                      (r01 − r02 , p1 , q1 ) = 0 
    →        →           →            →                                     
        r = r02 +ϕ p2 + θ q2                                              
                                                                                            → →              →      →            →             →         →       →      →
                                                                            ° [[ p1 , q1 ],[ p2 , q 2 ]] = o Ò ( r01 − r02 , p1 , q1 ) = 0 
                                                                            
                                                                            
                                                                                   → →              →      →
    |¯ˆººÓÈã Óº°ˆ  ¹ãº°}º°ˆË®  ([ p1 , q1 ],[ p 2 , q 2 ]) = 0 
    →        →           →            →
        r = r01 + ϕ p1 + θ q1 Ò
    →        →            →             →
        r = r02 + ϕ p2 + θ q 2 
    
                                                                               → → →                                                        → →
    È¯ÈããËã Óº°ˆ                            ¹ãº°}º°ˆË®  ( p , q , n ) = 0 ¹¯Ò‚°ãºmÒÒ ( n , r0 ) ≠ d 
    →       →          →          →            → →
        r = r0 + ϕ p + θ q Ò ( n , r ) = d 
    
                                                                               → → →                                                        → →
    vºm¹ÈËÓÒË                               ¹ãº°}º°ˆË®  ( p , q , n ) = 0 ¹¯Ò‚°ãºmÒÒ ( n , r0 ) = d 
    →       →          →          →            → →
        r = r0 + ϕ p + θ q Ò ( n , r ) = d 
    
                                                                                                                                                            →→                →
    |¯ˆººÓÈã Óº°ˆ  ¹ãº°}º°ˆË® ° v‚Ë°ˆm‚ˈ λ ≠ 0 ˆÈ}ºËˆº [ p, q ] = λ n 
    →    →      →     →      → →            
     r = r0 + ϕ p + θ q Ò ( n , r ) = d  
                                                    →→ →          →
                                            ° [[ p, q ], n ] = o 
                                            
                                            
             
             
                Òjisq|j|ˆÓº°ÒˆËã ÓÈ«º¯ÒËӈÈÒ«¹ãº°}º°ˆË®m¹¯º°ˆ¯ÈÓ°ˆmË
             
             

Страницы