Аналитическая геометрия и линейная алгебра. Умнов А.Е. - 216 стр.

UptoLike

ВУЗ: 

МФТИ | Москва

Составители: 

Рубрика: 


Ë} ÒÒ}ÈÁË ¯©m©° Ë®äÈËäÈÒ}Òlnj
ÙkÓÈãÒÒË°}È«˺äË¯Ò«ÒãÒÓË®ÓÈ«ÈãË¯Èµ

äÓºmkp
|¹¯ËËãËÓÒË

Íévqoknlntqnu ãÒÓˮӺº ÁÓ}ÒºÓÈãÈ
fx
()
ÓÈÒ°ãº
λ
ÓÈÏ©mÈË°«
ÁÓ}ÒºÓÈã°Èm«Ò®m°ººmË°mÒË}Èκä
x∈
Λ
Ò°ãº
λ
fx()

ËääÈ

¯ºÒÏmË
ËÓÒË ãÒÓˮӺ
º ÁÓ}
ÒºÓÈãÈ ÓÈ
Ò°ãº «mã«Ë°« ãÒÓˮөä
ÁÓ}ÒºÓÈãºä ã«}ºº¯ººm©¹ºãÓ«°«
Λ∈∀x
°ººÓºËÓÒ«
αβ αβ
αβ α β
ααα
(())()(); () ();
( ) () () () ;
( () ()) () () .
fx fx fx fx
fx fx fx
fx gx fx gx
==
+=+
+= +
1
iº}ÈÏÈËã°mº
m˯ÎËÓÒËãËää©¹¯ºm˯«Ë°«Ó˹º°¯Ë°mËÓÓº
˺¯ËäÈ

lÓºÎË°mº m°Ë² ãÒÓˮө² ÁÓ}ÒºÓÈãºm ÏÈÈÓÓ©² m ãÒÓˮӺä
¹¯º°¯ÈÓ°mË
Λ
 «mã«Ë°« ãÒÓˮөä ¹¯º°¯ÈÓ°mºä ººÏÓÈ
ÈËä©ä
+
Λ
iº}ÈÏÈËã°mº
vãËËÒÏº¹¯ËËãËÓÒ®ÒãËää
|¹¯ËËãËÓÒË

ÒÓˮӺË ¹¯º°¯ÈÓ°mº
+
Λ
ãÒÓˮө²ÁÓ}ÒºÓÈãºm ÏÈÈÓÓ©² m
Λ

ÓÈÏ©mÈË°«lkvpxzknttuÒãÒxvwé¹nttu¹¯º°¯ÈÓ°m
Λ

¯Ë°ÈmãËÓÒËãÒÓˮӺºÁÓ}ÒºÓÈãÈm
n
Λ
°m
n
Λ
ÈÓ ÈÏÒ°
},...,,{
21
n
ggg
Ò¹° }ºº¯ÒÓÈÓºË¹¯Ë°ÈmãËÓÒË ªãË
äËÓÈãÒÓˮӺº¹¯º°¯ÈÓ°mÈÒäËËmÒ
∑
=
=
n
i
ii
gx
1
ξ
ºÈm°ÒããÒÓˮӺ°ÒÁÓ}
ÒºÓÈãÈ°¹¯ÈmËãÒm©°ººÓºËÓÒ«
fx f g fg
ii
i
n
ii ii
i
n
i
n
() ( ) ( )== =
===
∑∑∑
ξ
ξ
φ
ξ
111

Ë
φ
ii
fg i n==(), [,]1
Ò°ãÈ ÓÈÏ©mÈËä©Ë rvuwvtntzjuq sqtnptvmv {ytr|qvtjsj k
ljttvuijoqxn
 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



  |¹¯ËËãËÓÒË      Íévqoknlntqnu ãÒÓˮӺº Á‚Ó}ÒºÓÈãÈ f ( x )  ÓÈ Ò°ãº λ ÓÈÏ©mÈˈ°«
  
                    Á‚Ó}ÒºÓÈã°ˆÈm«Ò®m°ººˆmˈ°ˆmÒË}Èκä‚x∈ΛÒ°ãºλ f ( x ) 
          
          
          
  ËääÈ            ¯ºÒÏmËËÓÒË ãÒÓˮӺº Á‚Ó}ÒºÓÈãÈ ÓÈ Ò°ãº «mã«Ëˆ°« ãÒÓˮөä
             Á‚Ó}ÒºÓÈãºäã«}ºˆº¯ººm©¹ºãÓ« ˆ°« ∀x ∈ Λ °ººˆÓºËÓÒ«
  
                    
                                                   α ( β f ( x )) = (α β ) f ( x ) ; 1 f ( x ) = f ( x ) ;
                                                  (α + β ) f ( x ) = α f ( x ) + β f ( x ) ;               
                                                  α ( f ( x ) + g ( x )) = α f ( x ) + α g ( x ) .
          
  iº}ÈÏȈËã°ˆmº
    
         ˆm˯ÎËÓÒËãËä䩹¯ºm˯«Ëˆ°«Ó˹º°¯Ë°ˆmËÓÓº
          
          
          
 ‘˺¯ËäÈ       lÓºÎË°ˆmº m°Ë² ãÒÓˮө² Á‚Ó}ÒºÓÈãºm ÏÈÈÓÓ©² m ãÒÓˮӺä
         ¹¯º°ˆ¯ÈÓ°ˆmË Λ  «mã«Ëˆ°« ãÒÓˮөä ¹¯º°ˆ¯ÈÓ°ˆmºä º­ºÏÓÈÈËä©ä
                         Λ+ 
        
  iº}ÈÏȈËã°ˆmº
   
      vãË‚ˈÒϺ¹¯ËËãËÓÒ®ÒãËää
        
        
        
 |¹¯ËËãËÓÒË            ÒÓˮӺË ¹¯º°ˆ¯ÈÓ°ˆmº Λ+  ãÒÓˮө² Á‚Ó}ÒºÓÈãºm ÏÈÈÓÓ©² m Λ 
 
                         ÓÈÏ©mÈˈ°«lkvpxzkntt€u ÒãÒxvwé¹ ntt€u ¹¯º°ˆ¯ÈÓ°ˆm‚ Λ 
            
            
            
¯Ë°ˆÈmãËÓÒËãÒÓˮӺºÁ‚Ó}ÒºÓÈãÈm Λ 
                                                                      n
            
            
            ‚°ˆ  m Λn  ÈÓ ­ÈÏÒ° {g1 , g 2 ,..., g n }  Ò ¹‚°ˆ  }ºº¯ÒÓȈӺË ¹¯Ë°ˆÈmãËÓÒË ªãË
                                                                             n
äËӈÈãÒÓˮӺº¹¯º°ˆ¯ÈÓ°ˆmÈÒäËˈmÒ x =                                 ∑ ξ i g i ‘ºÈm°Òã‚ãÒÓˮӺ°ˆÒÁ‚Ó}
                                                                            i =1
ÒºÓÈãÈ°¹¯ÈmËãÒm©°ººˆÓº ËÓÒ«
       
                                                                n                 n                 n
                                                f ( x ) = f ( ∑ ξ i gi ) = ∑ ξ i f ( g i ) = ∑ φ i ξ i 
                                                               i =1              i =1              i =1
            
Ë φ i = f ( g i ) , i = [1, n]   Ò°ãÈ ÓÈÏ©mÈËä©Ë rvuwvtntzjuq sqtnptvmv {ytr|qvtjsj k
ljttvuijoqxn
       

Страницы