Аналитическая геометрия и линейная алгебра. Умнов А.Е. - 259 стр.

UptoLike

ВУЗ: 

МФТИ | Москва

Составители: 

Рубрика: 

cÈÏËã
 

pm}ãÒºmº¹¯º°¯ÈÓ°mº
vÈ亰º¹¯«ÎËÓÓ©Ëº¹Ë¯Èº¯©
|¹¯ËËãËÓÒË

ÒÓˮө® º¹Ë¯Èº¯
R
 Ë®°mÒ® m Ëm}ãÒºmºä ¹¯º°¯ÈÓ°mË
E

ÓÈÏ©mÈË°«xjuvxvwé¹nttuË°ãÒ ã«
∀∈xy E,
ÒäËËäË°º¯ÈmËÓ°mº
(
,) (,
)Rx y x Ry=

¯Òä˯

{Ëm}ãÒºmºä¹¯º°¯ÈÓ°mËº¹Ë¯Èº¯©mÒÈ

AA
+
+


AA
+
Ò

AA
+

°È亰º¹¯«ÎËÓÓ©äÒã«ãººãÒÓˮӺºº¹Ë¯Èº¯È
A

iË®°mÒËãÓºã«º¹Ë¯Èº¯È

AA
+
Óȹ¯Òä˯ÒäËËäº¹¯Ò
∀∈
xy E,
(

,) (
,
)(,

)
A Ax y Ax Ay x A Ay
++
==
 º}È Ò °ãËË ˺ °È亰º¹¯«ÎËÓ
Óº°
vmº®°mÈ °È亰º¹¯«ÎËÓÓ©² º¹Ë¯Èº¯ºm °Áº¯äãÒ¯Ëä m mÒË °ãËÒ²
m˯ÎËÓÒ®
ËääÈ

ÒÓˮө®º¹Ë¯Èº¯
R
m
E
n
«mã«Ë°«°È亰º¹¯«ÎËÓÓ©äºÈÒºã}º
ºÈ}ºÈ˺äÈ¯ÒÈm}Èκäº¯ºÓº¯äÒ¯ºmÈÓÓºäÈÏÒ°Ë°ÒääË
¯ÒË°}È«
iº}ÈÏÈËã°mº
jÏº¹¯ËËãËÓÒ«ÒÁº¯äã©

T
RR
g
g
g
g
+
−
=
ΓΓ
1
ã«ÓË}ºº¯ººº¯º
Óº¯äÒ¯ºmÈÓÓºº ÈÏÒ°È
{ , ,..., }
ee e
n
12

T
RR
ee
+
=
Ò°ã˺mÈËãÓº

T
RR
ee
=
m°Òã°È亰º¹¯«ÎËÓÓº°Òº¹Ë¯Èº¯È
A

˯ˮËä}¯ºäº¯ºÓº¯äÒ¯ºmÈÓÓºäÈÏÒ°
{ , ,..., }
′′ ′ee e
n
12
lÈ¯ÒÈ¹Ë¯Ë
²ºÈ
S
 }È} ©ãº ¹º}ÈÏÈÓº m ¹ º¯ººÓÈãÓÈ« º Ë° ã« ÓËË
SS
−
=
1T
ºªºä
(
)(
)
()

.
T
T
T
T
T
T
T
T
T
T
T
RSRS SRSSRS
SRS SRS S RS R
ee e e
ee ee
′
−
−
′
=== =
====
1
1
ËääÈº}ÈÏÈÓÈ

cÈÏËã
pm}ãÒºmº¹¯º°ˆ¯ÈÓ°ˆmº



vÈ亰º¹¯«ÎËÓө˺¹Ë¯Èˆº¯©
           
           
           
    |¹¯ËËãËÓÒË          ÒÓˮө® º¹Ë¯Èˆº¯ R  Ë®°ˆm‚ Ò® m Ëm}ãÒºmºä ¹¯º°ˆ¯ÈÓ°ˆmË E
                  ÓÈÏ©mÈˈ°«xjuvxvwé¹ ntt€uË°ãÒã« ∀x , y ∈ E ÒäËˈäË°ˆº¯ÈmËÓ°ˆmº
                             , y ) = ( x , Ry
                          ( Rx               ) 
           
           
    ¯Òä˯               {Ëm}ãÒºmºä¹¯º°ˆ¯ÈÓ°ˆm˺¹Ë¯Èˆº¯©mÒÈ A + A +  AA
                                                                                   + Ò A + A ­‚‚ˆ
    
                          °È亰º¹¯«ÎËÓÓ©äÒã«ã ­ººãÒÓˮӺºº¹Ë¯Èˆº¯È A 
                          
                          iË®°ˆm҈Ëã Ӻ㫺¹Ë¯Èˆº¯È A + A Óȹ¯Òä˯ÒäËË䈺¹¯Ò ∀x , y ∈ E 
                          ( A + Ax
                                  , y ) = ( Ax
                                              , Ay
                                                  ) = ( x , A + Ay
                                                                   )  ºˆ}‚È Ò °ãË‚ˈ ˺ °È亰º¹¯«ÎËÓ
                          Óº°ˆ 
      
      
      
      vmº®°ˆmÈ °È亰º¹¯«ÎËÓÓ©² º¹Ë¯Èˆº¯ºm °Áº¯ä‚ãÒ¯‚Ëä m mÒË °ãË‚ Ò²
‚ˆm˯ÎËÓÒ®
      
      
 ËääÈ              ÒÓˮө®º¹Ë¯Èˆº¯ R m E n «mã«Ëˆ°«°È亰º¹¯«ÎËÓө䈺ÈÒˆºã }º
             ˆºÈ}ºÈ˺äȈ¯ÒÈm}Èκ亯ˆºÓº¯äÒ¯ºmÈÓÓºä­ÈÏÒ°Ë°Òääˈ
                     ¯ÒË°}È«

  iº}ÈÏȈËã°ˆmº
   
   
                                                                                                     −1
           jϺ¹¯ËËãËÓÒ«ÒÁº¯ä‚ã© R +                                                         R
                                                                                                               T

                                                                                        g
                                                                                            = Γ      g         g
                                                                                                                    Γ       g
                                                                                                                                ã«ÓË}ºˆº¯ººº¯ˆº

                                                                                                      R + e = R
                                                                                                                            T
           Óº¯äÒ¯ºmÈÓÓºº                    ­ÈÏÒ°È                 {e1 , e2 ,..., en }                                  e
                                                                                                                                        Ò        °ã˺mȈËã Óº

               R e = R         m°Òã‚°È亰º¹¯«ÎËÓÓº°ˆÒº¹Ë¯Èˆº¯È A 
                             T
                             e
           
           Ë¯Ë®Ëä}¯‚ºä‚º¯ˆºÓº¯äÒ¯ºmÈÓӺ䂭ÈÏÒ°‚ {e1′ , e2′ ,..., en′ } lȈ¯Òȹ˯Ë
           ²ºÈ         S  }È} ­©ãº ¹º}ÈÏÈÓº m ¹ º¯ˆººÓÈã ÓÈ« ˆº Ë°ˆ  ã« ÓËË
                   −1            T
               S        = S           ºªˆºä‚
           
                                                  −1
                                 R                     R                                  R                                  R
                                      T                                                 T                               T            T              T
                                      e′
                                           =( S                  e
                                                                     S )T = ( S                  e
                                                                                                     S )T = S                        e
                                                                                                                                         ( S            )T =
                                                                                                          −1
                                                                                                                                                               
                                                       R                          R                          R           S = R
                                                  T          T                 T
                                           = S               e
                                                                     S = S              e
                                                                                            S = S                   e                          e′
                                                                                                                                                        .
      
      
      ËääȺ}ÈÏÈÓÈ
           

Страницы