Аналитическая геометрия и линейная алгебра. Умнов А.Е. - 24 стр.

UptoLike

ВУЗ: 

МФТИ | Москва

Составители: 

Рубрика: 

28
Ë} ÒÒ}ÈÁË ¯©m©° Ë®äÈËäÈÒ}Òlnj
ÙkÓÈãÒÒË°}È«˺äË¯Ò«ÒãÒÓË®ÓÈ«ÈãË¯Èµ
äÓºmkp
º°¯ºÒäÓË¯ÒmÒÈãÓãÒÓË®Ó}ºäÒÓÈÒmË}º¯ºm
},...,,{
21
→→→
n
aaa
mÏ«mm
}ÈË°mË¹Ë¯m©²
k
}ºªÁÁÒÒËÓºmÒ°ãÈ
],1[,
ki
i
=
λ
ÒÓãÒm}ÈË°mËº°Èã
Ó©²ºÈ¹ºãÒäº
→
+=
→
=
→
=
→
=⋅+=
∑∑∑
oaaa
n
ki
i
k
i
ii
n
i
ii
111
0
λλ

˺¯ËäÈº}ÈÏÈÓÈ

vãË°mÒË

p°ãÒ °¯ËÒ mË}º¯ºm
},...,,{
21
→→→
n
aaa
ÒäËË°« ²º« © ºÒÓ ÓãËmº® º
mË}º¯©
},...,,{
21
→→→
n
aaa
ãÒÓˮӺÏÈmÒ°Òä©
rÈÏÒ°zºº¯ÒÓÈ©mË}º¯ÈmÈÏÒ°Ë
|¹¯ËËãËÓÒË

Èjoqxvutjwé¹uvpÓÈÏ©mÈË°«ãº®ÓËÓãËmº®mË}º¯¹¯ÒÓÈãËÎÈ
Ò®ªº®¹¯«äº®
Èjoqxvu tj wsvxrvxzqÓÈÏ©mÈË°«ãÈ« ¹È¯È ãÒÓˮӺ ÓËÏÈmÒ°Ò䩲
mË}º¯ºm¹¯ÒÓÈãËÎÈÒ²ªº®¹ãº°}º°Ò
ÈjoqxvukwévxzéjtxzknÓÈÏ©mÈË°«ãÈ«¯º®}ÈãÒÓˮӺÓËÏÈmÒ°Ò
䩲mË}º¯ºm
|¹¯ËËãËÓÒË

rÈÏÒ° ÓÈÏ©mÈË°« vézvmvtjstu Ë°ãÒ º¯ÈÏÒË ˺ mË}º¯© ¹º
¹È¯Óºº¯ººÓÈãÓ©mÏÈÒäÓº¹Ë¯¹ËÓÒ}㫯ө
|¹¯ËËãËÓÒË

|¯ººÓÈãÓ©®ÈÏÒ°ÓÈÏ©mÈË°«vézvtvéuqévkjttuË°ãÒº¯ÈÏ
ÒË˺mË}º¯©ÒäËËÒÓÒÓãÒÓ
¯º°¯ÈÓ°mËÓÓ©® ÈÏÒ° °º°ÈmãËÓÓ©® ÒÏ ãÒÓˮӺ ÓËÏÈmÒ°Ò䩲 mË}º¯ºm
→→→
321
,,
ggg
ËäººÏÓÈÈ
},,{
321
→→→
ggg
|¯ººÓÈãÓ©®ÒãÒº¯ºÓº¯äÒ¯ºmÈÓÓ©®ÈÏÒ°
°ãºmÒä°«ººÏÓÈÈ}È}
},,{
321
→→→
eee

˺¯ËäÈ

° ÈÓ ÈÏÒ°
},,{
321
→→→
ggg
 ºÈ ãº® mË}º¯
x
→
m ¹¯º°¯ÈÓ°mË
äºÎË ©¹¯Ë°ÈmãËÓ Ò ¹¯Òºä ËÒÓ°mËÓÓ©ä º¯ÈϺä m mÒË
→→→→
++=
321
gggx
γ
βα
Ë
αβ
γ
,,
-
ÓË}ºº¯©ËÒ°ãÈ
28 Ë }  Ò Ò   } È Á Ë  ¯ ©   m © °  Ë ®   ä È ˆ Ë ä È ˆ Ò } Ò   l n ‘ j 
ÙkÓÈã҈ÒË°}È«˺äˈ¯Ò«ÒãÒÓË®ÓÈ«ÈãË­¯ÈµäÓºmkp



                                                                                                                → →          →
          º°ˆ¯ºÒä Óˈ¯ÒmÒÈã ӂ  ãÒÓˮӂ  }ºä­ÒÓÈÒ  mË}ˆº¯ºm {a1, a2 ,..., an }  mÏ«m m
          }ÈË°ˆm˹˯m©² k }ºªÁÁÒÒËӈºmÒ°ãÈ λ i , i = [1, k ] ÒӂãÒm}ÈË°ˆm˺°ˆÈã 
                                                    n       →      k       →        n       →    →
          Ó©²‘ºÈ¹ºã‚Ò䈺                 ∑ λ i ai = ∑ λ i ai +           ∑ 0 ⋅ ai = o 
                                                   i =1           i =1           i = k +1
          
      ‘˺¯ËäȺ}ÈÏÈÓÈ


                                                               → →          →
    vãË°ˆmÒË           p°ãÒ °¯ËÒ mË}ˆº¯ºm {a1, a2 ,..., an }  ÒäËˈ°« ²ºˆ« ­© ºÒÓ ӂãËmº® ˆº
    
                                         → →            →
                         mË}ˆº¯© {a1, a2 ,..., an } ãÒÓˮӺÏÈmÒ°Òä©
              
              
              
              
rÈÏÒ°zºº¯ÒÓȈ©mË}ˆº¯Èm­ÈÏÒ°Ë
              
              
              
    |¹¯ËËãËÓÒË         Èjoqxvutjwé¹uvpÓÈÏ©mÈˈ°«ã ­º®ÓËӂãËmº®mË}ˆº¯¹¯ÒÓÈãËÎÈ
                  Ò®ªˆº®¹¯«äº®
                         
                         Èjoqxvu tj wsvxrvxzq ÓÈÏ©mÈˈ°« ã ­È« ¹È¯È ãÒÓˮӺ ÓËÏÈmÒ°Ò䩲
                         mË}ˆº¯ºm¹¯ÒÓÈãËÎȝҲªˆº®¹ãº°}º°ˆÒ
                         
                         ÈjoqxvukwévxzéjtxzknÓÈÏ©mÈˈ°«ã ­È«ˆ¯º®}ÈãÒÓˮӺÓËÏÈmÒ°Ò
                         䩲mË}ˆº¯ºm
              
    |¹¯ËËãËÓÒË         rÈÏÒ° ÓÈÏ©mÈˈ°« vézvmvtjst€u Ë°ãÒ º­¯Èς ÒË Ëº mË}ˆº¯© ¹º
                  ¹È¯Óºº¯ˆººÓÈã Ó© mÏÈÒäÓº¹Ë¯¹ËÓÒ}‚㫯ө 
              
    |¹¯ËËãËÓÒË         |¯ˆººÓÈã Ó©®­ÈÏÒ°ÓÈÏ©mÈˈ°«vézvtvéuqévkjtt€uË°ãÒº­¯Èς 
                  ÒË˺mË}ˆº¯©ÒäË ˆËÒÓÒӂ ãÒӂ
              
              
              ¯º°ˆ¯ÈÓ°ˆmËÓÓ©® ­ÈÏÒ° °º°ˆÈmãËÓÓ©® ÒÏ ãÒÓˮӺ ÓËÏÈmÒ°Ò䩲 mË}ˆº¯ºm
→ → →                                            → → →
g1, g 2 , g 3 ­‚Ë亭ºÏÓÈȈ  {g1, g 2 , g 3 } |¯ˆººÓÈã Ó©®ÒãÒº¯ˆºÓº¯äÒ¯ºmÈÓÓ©®­ÈÏÒ°
                                             → → →
‚°ãºmÒä°«º­ºÏÓÈȈ }È} {e1 , e 2 , e 3 } 
       
                                                           → → →                                               →
    ‘˺¯ËäÈ             ‚°ˆ  ÈÓ ­ÈÏÒ° {g1 , g 2 , g 3 }  ˆºÈ ã ­º® mË}ˆº¯ x  m ¹¯º°ˆ¯ÈÓ°ˆmË
    
                         äºÎˈ ­©ˆ  ¹¯Ë°ˆÈmãËÓ Ò ¹¯Òˆºä ËÒÓ°ˆmËÓÓ©ä º­¯ÈϺä m mÒË
                         →         →         →          →
                          x = α g1 + β g 2 + γ g 3 Ë α , β , γ -ÓË}ºˆº¯©ËÒ°ãÈ
              

Страницы