Аналитическая геометрия и линейная алгебра. Умнов А.Е. - 180 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
cÈÏËã
jspqshp~k{jvjl|vj
{jspqs|lc|vcksv{p
ÒÓˮөËº¹Ë¯Èº¯©
|¹¯ËËãËÓÒË

°}ÈκäªãËäËÓ
x
ãÒÓˮӺº¹¯º°¯ÈÓ°mÈ
Λ
¹º°ÈmãËÓm°º
ºmË°mÒË ËÒÓ°mËÓÓ©® ªãËäËÓ
y
ãÒÓˮӺº ¹¯º°¯ÈÓ°mÈ
∗
Λ
.
ºÈ
ºmº¯« º m
Λ
ÏÈÈÓ vwnéjzvé Ë®°mÒ® m
Λ
Ò ÒäËÒ®
ÏÓÈËÓÒ«m
∗
Λ
ººÏÓÈÈËä©®
xAy
ˆ
=

¯ÒªºäªãËäËÓ
y
ÓÈÏ©mÈË°«viéjovuªãËäËÓÈ
x
ÈªãËäËÓ
x
wév
viéjovuªãËäËÓÈ
y

zÈ}Òm¹º¹Ë¯Èº¯©¹º¯ÈÏËã«°«ÓÈvzviéjntq¹Ë°ãÒ
Λ⊄Λ
∗
Òwén
viéjovkjtq¹Ë°ãÒ
Λ⊆Λ
∗
{ÈãÓË®ËäÏÈÒ°}ãËÓÒËäº°ººººmº¯ËÓÓ©²°ãÈËm
Ë ¹¯Ë¹ºãÈÈ°« º
Λ⊆Λ
∗
 º Ë° ä© Ëä ¯È°°äÈ¯ÒmÈ ¹¯Ëº¯ÈϺmÈÓÒ«
Ë®°mÒËm
Λ

|¹¯ËËãËÓÒË

|¹Ë¯Èº¯
yAx
=
ÓÈÏ©mÈË°«sqtnptuË°ãÒã«ã©²
Λ∈
21
,,
xxx
Ò
ãººÒ°ãÈ
λ
ÒäËäË°º¯ÈmËÓ°mÈ
°
()

Ax x Ax Ax
12 1 2
+= +Ò
°
()
Ax Ax
λλ
=

¯Òä˯

°{ ¹¯º°¯ÈÓ°mË ä˯ө² mË}º¯ºm ãÒÓˮөä º¹Ë¯Èº¯ºä
«mã«Ë°«¹¯ÈmÒãº
2
1
2221
1211
2
1
ξ
ξ
η
η
aa
aa
=

°m«Ï©mÈËË mË}º¯¹¯ºº¯ÈÏ
2
1
ξ
ξ
=
x
° mË}º¯ºäº¯ÈϺä
2
1
η
η
=
y

 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



          
          
          
          
          
          
cÈÏËã
jspqshp~k{jvjl|v‘j
{jspqs|lc|v‘cksv‘{p
            
            
            
            
ÒÓˮө˺¹Ë¯Èˆº¯©
            
            
            
 |¹¯ËËãËÓÒË            ‚°ˆ }Èκ䂪ãËäËӈ‚ xãÒÓˮӺº¹¯º°ˆ¯ÈÓ°ˆmÈ Λ ¹º°ˆÈmãËÓm°º
 
                         ºˆmˈ°ˆmÒË ËÒÓ°ˆmËÓÓ©® ªãËäËӈ y ãÒÓˮӺº ¹¯º°ˆ¯ÈÓ°ˆmÈ Λ∗ . ‘ºÈ
                         ºmº¯«ˆ ˆº m Λ  ÏÈÈÓ vwnéjzvé Ë®°ˆm‚ Ò® m Λ Ò ÒäË Ò®
                         ÏÓÈËÓÒ«m Λ∗ º­ºÏÓÈÈËä©® y = Aˆ x 
                         

                         ¯ÒªˆºäªãËäËӈ yÓÈÏ©mÈˈ°«viéjovuªãËäËӈÈ xȪãËäËӈ xwév
                         viéjovuªãËäËӈÈy
            

            zÈ}Òm¹º¹Ë¯Èˆº¯©¹º¯ÈÏËã« ˆ°«ÓÈvzviéj ntq¹Ë°ãÒ Λ∗ ⊄ Λ Òwén
viéjovkjtq¹ Ë°ãÒ Λ∗ ⊆ Λ  { Èã ÓË® Ëä ÏÈ Ò°}ã ËÓÒËä º°º­º ººmº¯ËÓÓ©² °ã‚ÈËm
­‚ˈ ¹¯Ë¹ºãÈȈ °« ˆº Λ∗ ⊆ Λ  ˆº Ë°ˆ  ä© ­‚Ëä ¯È°°äȈ¯ÒmȈ  ¹¯Ëº­¯ÈϺmÈÓÒ«
Ë®°ˆm‚ ÒËm Λ 
        
        
 |¹¯ËËãËÓÒË                           ÓÈÏ©mÈˈ°«sqtnpt€uË°ãÒã«ã ­©² x, x , x ∈ Λ Ò
                         |¹Ë¯Èˆº¯ y = Ax                                           1 2
 
                         ã ­ººÒ°ãÈλÒäË ˆäË°ˆº¯ÈmËÓ°ˆmÈ
                         ° A ( x1 + x 2 ) = Ax
                                                                                  + Ax
                                                                                   1
                                                                                      Ò
                                                                                        2

                         ° A ( λ x ) = λ Ax
                                                                               
            
 ¯Òä˯                 °{ ¹¯º°ˆ¯ÈÓ°ˆmË ä˯ө² mË}ˆº¯ºm ãÒÓˮөä º¹Ë¯Èˆº¯ºä
                       «mã«Ëˆ°«¹¯ÈmÒãº
                                                                     η1   a   a   ξ1
                                                                        = 11 12       
                                                                     η2   a21 a22 ξ 2
                                                                                                  ξ1
                                 °m«Ï©mÈ ËË mË}ˆº¯¹¯ºº­¯ÈÏ x =                                    ° mË}ˆº¯ºäº­¯ÈϺä
                                                                                                  ξ2
                                        η1
                                 y=        
                                        η2
                             

Страницы