Аналитическая геометрия и линейная алгебра. Умнов А.Е. - 142 стр.

UptoLike

Составители: 

Рубрика: 


Ë} ÒÒ}ÈÁË ¯©m©° Ë®äÈËäÈÒ}Òlnj
ÙkÓÈãÒÒ˰}È«˺äË¯Ò«ÒãÒÓË®ÓÈ«ÈãË¯Èµ

äÓºmkp
Ë
M
0
 ÈÏÒ°Ó©® äÒÓº¯ È
DD
r
1
,...,
 ÓË}ºº¯©Ë ÈãË¯ÈÒ˰}ÒË
º¹ºãÓËÓÒ«ÓËÏÈmÒ°«ÒËº
i
vã˺mÈËãÓº
irriiij
αλαλαλα
+++= ...
2211

Ë
M
D
s
s
=
λ

i

˺¯ËäÈº}ÈÏÈÓÈ
|¹¯ËËãËÓÒË

vºã©
aa a
n
12
, ,...,
ËäÓÈÏ©mÈsqtnptvojkqxquuq˰ãÒ
°˰m ÓË ¯ÈmÓ©Ë ÓãºÓºm¯ËäËÓÓº Ò°ãÈ
λλ λ
12
, ,...,
n
È}ÒË
º
)0(,
11
>=
==
n
i
ii
n
i
i
oa
λλ

ËääÈ

iã«ººº©°ºã©°¯º}ÒäÈ¯Ò©©ãÒãÒÓˮӺÏÈmÒ°Òä©
äÒÓ˺²ºÒäºÒº°ÈºÓºº©ºÒÓÒÏÓÒ²©ããÒÓˮӺ®}ºä
ÒÓÈÒË®º°ÈãÓ©²
iº}ÈÏÈËã°mº
vºm¹ÈÈË°º}ÈÏÈËã°mºäãËää©
ËääÈ

p°ãÒºÒÓÒÏ °ºãºmäÈ¯Ò©˰ãÒÓË®ÓÈ« }ºäÒÓÈÒ« ÓË}ºº
¯ºº ¹ºäÓºÎ˰mÈ º°ÈãÓ©² º °ºã© ªº® äÈ¯Ò© ãÒÓˮӺ
ÏÈmÒ°Òä©
iº}ÈÏÈËã°mº
º ãËääË  äºÎÓº m˯ÎÈº °¯ËÒ °ºãºmäÈ¯Ò© ˰¹ºäÓº
Î˰mº ãÒÓˮӺ ÏÈmÒ°Ò䩲 sº ºÈ m ãÒÓˮӺ® }ºäÒÓÈÒÒ m°Ë² °ºãºm
äÈ¯Ò©ã«°ºãºmº¹ºãÓ«Ò²¹ºäÓºÎ˰mºãÒÓˮӺÏÈmÒ°Ò䩲äºÎÓº
¹ºãºÎÒ
λ
i
=0

väº}ÈÏÈËã°mº˺¯Ëä©
ËääÈº}ÈÏÈÓÈ
˺¯ËäÈ

iã«ººº©º¹¯Ë ËãÒËã©ã¯ÈmËÓÓãÓ˺²ºÒäºÒº°È
ºÓºº©˺°ºã©°¯º}Ò©ãÒãÒÓˮӺÏÈmÒ°Òä©äÒ
 Ë }  Ò Ò    } È Á Ë  ¯ ©   m © °  Ë ®   ä È ˆ Ë ä È ˆ Ò } Ò   l n ‘ j 
ÙkÓÈã҈Ò˰}È«˺äˈ¯Ò«ÒãÒÓË®ÓÈ«ÈãË­¯ÈµäÓºmkp



            Ë M ≠ 0   ­ÈÏÒ°Ó©® äÒÓº¯ È D1 ,..., Dr  ÓË}ºˆº¯©Ë ÈãË­¯ÈÒ˰}ÒË
                º¹ºãÓËÓÒ«ÓËÏÈmÒ°«Ò˺ˆ ivã˺mȈËã Óº α ij = λ 1α i1 + λ 2α i 2 + ... + λrα ir 
                                 Ds
                Ë λ s = −       ∀i
                                 M
        
        
     ‘˺¯ËäȺ}ÈÏÈÓÈ
            
            
            
 
 |¹¯ËËãËÓÒË            vˆºã­© a1 , a 2 ,..., a n ­‚ËäÓÈÏ©mȈ sqtnptvojkqxqu€uq˰ãÒ
 
                         °‚Ë°ˆm‚ ˆ ÓË ¯ÈmÓ©Ë ӂã  ºÓºm¯ËäËÓÓº Ò°ãÈ λ1 , λ2 ,..., λn  ˆÈ}ÒË
                                 n                             n
                         ˆº   ∑ λ i ai = o , ( ∑ λ i > 0 ) 
                                i =1                          i =1
            
            
            
 ËääÈ                  i㫈ººˆº­©°ˆºã­© °ˆ¯º}Ò äȈ¯Ò©­©ãÒãÒÓˮӺÏÈmÒ°Òä©
                  äÒÓ˺­²ºÒäºÒº°ˆÈˆºÓºˆº­©ºÒÓÒÏÓÒ²­©ããÒÓˮӺ®}ºä
                         ­ÒÓÈÒË®º°ˆÈã Ó©²
            
            
  iº}ÈÏȈËã°ˆmº
    
         vºm¹ÈÈˈ°º}ÈÏȈËã °ˆmºäãËää©
           
           
           
 ËääÈ           p°ãÒ ºÒÓ ÒÏ °ˆºã­ºm äȈ¯Ò© ˰ˆ  ãÒÓË®ÓÈ« }ºä­ÒÓÈÒ« ÓË}ºˆº
           ¯ºº ¹ºäÓºÎ˰ˆmÈ º°ˆÈã Ó©² ˆº °ˆºã­© ªˆº® äȈ¯Ò© ãÒÓˮӺ
                  ÏÈmÒ°Òä©
           
           
  iº}ÈÏȈËã°ˆmº
              
         º ãËääË  äºÎÓº ‚ˆm˯ÎȈ  ˆº °¯ËÒ °ˆºã­ºm äȈ¯Ò© ˰ˆ  ¹ºäÓº
         Î˰ˆmº ãÒÓˮӺ ÏÈmÒ°Ò䩲 sº ˆºÈ m ãÒÓˮӺ® }ºä­ÒÓÈÒÒ m°Ë² °ˆºã­ºm
         äȈ¯Ò©ã«°ˆºã­ºmº¹ºãÓ« Ò²¹ºäÓºÎ˰ˆmºãÒÓˮӺÏÈmÒ°Ò䩲äºÎÓº
         ¹ºãºÎ҈ λi=0
         
          väº}ÈÏȈËã °ˆmºˆËº¯Ëä© 
         
    ËääȺ}ÈÏÈÓÈ
           
           
           
 ‘˺¯ËäÈ         i㫈ººˆº­©º¹¯ËËã҈Ëã ­©ã¯ÈmËÓӂã Ó˺­²ºÒäºÒº°ˆÈ
           ˆºÓºˆº­©Ëº°ˆºã­© °ˆ¯º}Ò ­©ãÒãÒÓˮӺÏÈmÒ°Òä©äÒ