Аналитическая геометрия и линейная алгебра. Умнов А.Е. - 251 стр.

UptoLike

Составители: 

Рубрика: 

cÈÏËã
 

pm}ãÒºmº¹¯º°¯ÈÓ°mº
 |¯ººÓÈãÓ©Ë º¹ºãÓËÓÒ« Ò º¯ººÓÈãÓ©Ë ¹¯ºË}ÒÒ m
Ëm}ãÒºmºä¹¯º°¯ÈÓ°mË
°m
E
ÏÈÈÓº ÓË}ºº¯ºË ¹º¹¯º°¯ÈÓ°mº
E
1
 cȰ°äº¯Òä äÓºÎ˰mº
E
2
E
ªãËäËÓºm
x
º¯ººÓÈãÓ©²m°ËäªãËäËÓÈäÒÏ
E
1

|¹¯ËËãËÓÒË

{ Ëm}ãÒºmºä ¹¯º°¯ÈÓ°mË
E
°ºmº}¹Óº° ªãËäËÓºm
x
È}Ò² º
0),(
=yx
ã«
∀∈ yE E
1
ÓÈÏ©mÈË°« vézvmvtjstu lvwvstntqnu
äÓºÎ˰mÈ
E
1

˺¯ËäÈ

|¯ººÓÈãÓºËº¹ºãÓËÓÒË
k
ä˯Ӻº¹º ¹¯º°¯ÈÓ°mÈ
n
EE
1
«mã«
Ë°«¹º¹¯º°¯ÈÓ°mºä¯ÈÏä˯Ӻ°Ò
n
k

iº}ÈÏÈËã°mº
°m
E
n
°º°ÈÓȯÓ©ä°}È㫯өä¹¯ºÒÏmËËÓÒËäÈÓº¯ºÓº¯äÒ¯ºmÈÓÓ©®
ÈÏÒ°Ò¹°
E
2
º¯ººÓÈãÓºËº¹ºãÓËÓÒË}
E
1
{©˯ËäÓË}ºº¯©®ÈÏÒ°m
E
1
{, ,..., }
gg g
k
12
 ºÈ ÒÏ °ãºmÒ« º¯ººÓÈãÓº°Ò ¹¯ºÒÏmºãÓºº ªãËäËÓÈ
xE
2
}ÈκäªãËäËÓ
E
1
°ãËË°ä˺¯Ëäº
(, ) ; [,]xg i n
i
==
01
ÒãÒÎË
m}ºº¯ÒÓÈÓº®Áº¯äË
=+++
=+++
=+++
0...
....................................
0...
0...
2211
2222121
1212111
nknkk
nn
nn
ξ
ε
ξ
ε
ξ
ε
ξ
ε
ξ
ε
ξ
ε
ξ
ε
ξ
ε
ξ
ε
Ë
],1[;
...
2
1
kjg
jn
j
j
j
==
ε
ε
ε
Ò
n
x
ξ
ξ
ξ
...
2
1
=

wÈ ºÓº¯ºÓÈ« °Ò°ËäÈ ãÒÓˮө² ¯ÈmÓËÓÒ® ÓËÒÏm˰Ó©Ë m }ºº¯º® ˰
}ºä¹ºÓËÓ© ªãËäËÓÈ
x
 º¹¯ËËã«È« º¯ººÓÈãÓºË º¹ºãÓËÓÒË
E

 ÒäËË
¯ÈÓ
k
m°ÒããÒÓˮӺ®ÓËÏÈmÒ°Ò亰ÒªãËäËÓºm
{, ,..., }gg g
k
12
ºÈ¹º˺
¯ËäË   ÓËË ˰
n
k
ãÒÓˮӺ ÓËÏÈmÒ°Ò䩲 ¯ËËÓÒ® º¯ÈÏÒ² ÈÏÒ°
¹º¹¯º°¯ÈÓ°mÈ
E

˺¯ËäÈº}ÈÏÈÓÈ
ËÒä°«˹˯m°¹¯ÈmËãÒmº°Ò°ãË˺m˯ÎËÓÒ«
cÈÏËã
pm}ãÒºmº¹¯º°ˆ¯ÈÓ°ˆmº



          |¯ˆººÓÈã Ó©Ë º¹ºãÓËÓÒ« Ò º¯ˆººÓÈã Ó©Ë ¹¯ºË}ÒÒ m
                 Ëm}ãÒºmºä¹¯º°ˆ¯ÈÓ°ˆmË
          
          
          
        ‚°ˆ  m E ÏÈÈÓº ÓË}ºˆº¯ºË ¹º¹¯º°ˆ¯ÈÓ°ˆmº E1 cȰ°äºˆ¯Òä äÓºÎ˰ˆmº E2⊂E
ªãËäËӈºmxº¯ˆººÓÈã Ó©²m°ËäªãËäËӈÈäÒÏE1
          
          
          
 |¹¯ËËãËÓÒË    { Ëm}ãÒºmºä ¹¯º°ˆ¯ÈÓ°ˆmË E °ºmº}‚¹Óº°ˆ  ªãËäËӈºm x ˆÈ}Ò² ˆº
 
                  ( x, y ) = 0  ã« ∀y ∈ E1 ⊂ E  ÓÈÏ©mÈˈ°« vézvmvtjst€u lvwvstntqnu
                          äÓºÎ˰ˆmÈE1
           
           
           
 ‘˺¯ËäÈ                |¯ˆººÓÈã Ӻ˺¹ºãÓËÓÒË kä˯Ӻº¹º¹¯º°ˆ¯ÈÓ°ˆmÈ E1 ⊂ E n «mã«
 
               ˈ°«¹º¹¯º°ˆ¯ÈÓ°ˆmºä¯ÈÏä˯Ӻ°ˆÒ nk 

  iº}ÈÏȈËã°ˆmº
      
           ‚°ˆ m E n °º°ˆÈÓȯˆÓ©ä°}È㫯ө乯ºÒÏmËËÓÒËäÈÓº¯ˆºÓº¯äÒ¯ºmÈÓÓ©®
           ­ÈÏÒ°Ò¹‚°ˆ  E2º¯ˆººÓÈã Ӻ˺¹ºãÓËÓÒË} E1 {©­Ë¯ËäÓË}ºˆº¯©®­ÈÏÒ°m E1
           {g1 , g 2 ,..., g k }  ‘ºÈ ÒÏ ‚°ãºmÒ« º¯ˆººÓÈã Óº°ˆÒ ¹¯ºÒÏmºã Óºº ªãËäËӈÈ x∈E2
           }Èκ䂪ãËäËӈ‚ E1°ãË‚ˈ °äˆËº¯Ëä‚ ˆº ( x , gi ) = 0 ; i = [1, n] ÒãÒÎË
           m}ºº¯ÒÓȈӺ®Áº¯äË
           
           
                           ε 11ξ1 + ε 12ξ 2 + ... + ε 1nξ n = 0                ε j1                                        ξ1
                          ε ξ + ε ξ + ... + ε ξ = 0                            ε j2                                        ξ
                           21 1 22 2
                          
                                                        2n n
                                                                   Ë g j =      ;                  j = [1, k ] Ò x = 2 
                           ....................................                 ...                                        ...
                          ε k 1ξ1 + ε k 2ξ 2 + ... + ε knξ n = 0              ε jn                                        ξn
           
           
           wˆÈ ºÓº¯ºÓÈ« °Ò°ˆËäÈ ãÒÓˮө² ‚¯ÈmÓËÓÒ® ÓËÒÏm˰ˆÓ©Ë m }ºˆº¯º® ˰ˆ 
           }ºä¹ºÓËӈ© ªãËäËӈÈ x  º¹¯ËËã« È« º¯ˆººÓÈã ÓºË º¹ºãÓËÓÒË E  ÒäËˈ
           ¯ÈÓ km°Òã‚ãÒÓˮӺ®ÓËÏÈmÒ°Ò亰ˆÒªãËäËӈºm {g1 , g 2 ,..., g k } ‘ºÈ¹ºˆËº
        ¯ËäË  ‚ ÓËË ˰ˆ  nk ãÒÓˮӺ ÓËÏÈmÒ°Ò䩲 ¯Ë ËÓÒ® º­¯Èς Ò² ­ÈÏÒ°
        ¹º¹¯º°ˆ¯ÈÓ°ˆmÈE
        
        
     ‘˺¯ËäȺ}ÈÏÈÓÈ
        
        
        ­ËÒä°«ˆË¹Ë¯ m°¹¯ÈmËãÒmº°ˆÒ°ãË‚ Ëº‚ˆm˯ÎËÓÒ«