Аналитическая геометрия и линейная алгебра. Умнов А.Е. - 334 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
° vÒ°ËäÈãÒÓˮө²¯ÈmÓËÓÒ®mÒÈ
=+++
=+++
=+++
nnn
n
nn
n
n
n
n
β
ξ
α
ξ
α
ξ
α
β
ξ
α
ξ
α
ξ
α
β
ξ
α
ξ
α
ξ
α
...
.............................................
...
...
2
2
1
1
2222
2
12
1
1121
2
11
1
° Ëºä °ºãÈËÓÒ® º ËÓϺ¯Ó©² ººÏÓÈËÓÒ«² ÏȹҰ©
mÈË°«¹¯º°º}È}
kik
i
β
ξ
α
=

j°¹ºãÏ«°ºãÈËÓÒ«ºËÓϺ¯Ó©²ººÏÓÈËÓÒ«²Ò¹¯ÒÓÒäÈ«mºmÓÒäÈÓÒËº
Ò°ãÈ
ij
σ
Ò
ij
τ
}ºä¹ºÓËÓ©äÈ¯Ò¹¯«äººÒº¯ÈÓºº¹Ë¯Ë²ºÈäËÎÈÏÒ°ÈäÒ
},...,,{
21
n
ggg
Ò
},...,,{
21
n
ggg
«mã«°«È}ÎË}ºä¹ºÓËÓÈäÒËÓϺ¯ºmÒ¹È°Áº¯
äãÒ¯Ëä
|¹¯ËËãËÓÒË
¯
rËäºmº¯ÒºmmË˰mËÓÓºäãÒÓˮӺä¹¯º°¯ÈÓ°mË
n
Λ
º¹¯Ë
ËãËÓzntovézqwj
),(
pq
T
éjorvtzéjkjéqjtztpÒ
S
éjorvkjéqjtz
tp˰ãÒm
n
Λ
ÏÈÈÓºË}}ºº¯©®m}ÈκäÈÏÒ°Ë²È¯È}˯ÒÏË°«
¹º¯«ºËÓÓ©äÓÈº¯ºä
n
pq
+
Ò°Ëã
q
p
jjj
iii
...
...
2
21
1
ξ
Ë
jm q
m
;[,]
=
1
}ºÓ
¯ÈmȯÒÈÓÓ©Ë ÒÓË}°© Ò
ik p
k
;[,]
=
1
 }ºmȯÒÈÓÓ©Ë ÒÏäËÓ«
Ò˰« ¹¯Ò ¹Ë¯Ë²ºË º ÈÏÒ°È
},...,,{
21
n
ggg
}ÈÏÒ°
},...,,{
21
n
ggg
¹º
ÏÈ}ºÓ
=
q
p
jjj
iii
...
...
2
21
1
ξ
p
p
i
i
i
i
i
i
σσσ
...
2
2
1
1
q
q
j
j
j
j
j
j
τττ
...
2
2
1
1
q
p
jjj
iii
...
...
2
21
1
ξ

|¹¯ËËãËÓÒË
¯
Ò°ãº
)(
pq +
ÓÈÏ©mÈË°« kjsntztvxzí ÒãÒ éjtmvu ËÓϺ¯È
pq
iiijjj
......
212
1
ξ

|¹¯ËËãËÓÒË
¯
imÈËÓϺ¯ÈÓÈÏ©mÈ°«éjktuq˰ãÒºÓÒºÓººÒººÎËÒ¹ÈÒ
mºm°Ë²ÈÏҰȲÒäË¯ÈmÓ©Ë}ºä¹ºÓËÓ©
~ÈäËÈÓÒ«
° iã« ¯ÈmËÓ°mÈ ËÓϺ¯ºm ºÓºº Ò¹È º°ÈºÓº º© Ò² }ºä¹ºÓËÓ©
©ãÒ ¯ÈmÓ© ãÒ m ÓË}ºº¯ºä ÈÏÒ°Ë È} }È} ÒÏ Áº¯äã ¹Ë¯Ë°ËÈ
}ºä¹ºÓËÓºm°ãËËºªÒËÓϺ¯©ÒäË¯ÈmÓ©Ë}ºä¹ºÓËÓ©
Òmãºä¯ºäÈÏÒ°Ë
°p°ãÒ ºË} ²È¯È}˯ÒÏË°« ºÓÒä Ò°ãºä ¹¯ÒËä ÓË ÏÈmÒ°«Òä º
m©º¯ÈÈÏÒ°Èº˺äºÎÓº°ÒÈËÓϺ¯ºäÒ¹È
 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



                               ° vÒ°ˆËäÈãÒÓˮө²‚¯ÈmÓËÓÒ®mÒÈ
                                          

                                                                                        α11ξ 1 + α 12ξ 2 + ... + α 1nξ n = β 1
                                                                                        2 1
                                                                                       α1 ξ + α 22ξ 2 + ... + α n2ξ n = β 2
                                                                                                                                      
                                                                                        .............................................
                                                                                       α nξ 1 + α nξ 2 + ... + α nξ n = β n
                                                                                        1            2                 n
                                          

                                                     ° ‚ˈºä °ºãÈ ËÓÒ® º ˆËÓϺ¯Ó©² º­ºÏÓÈËÓÒ«² ÏȹҰ©
                                                     mÈˈ°«¹¯º°ˆº}È} α ik ξ i = β k 
            
            
            j°¹ºã ς«°ºãÈ ËÓÒ«ºˆËÓϺ¯Ó©²º­ºÏÓÈËÓÒ«²Ò¹¯ÒÓÒäÈ«mºmÓÒäÈÓÒˈº
Ò°ãÈ σ ij Ò τ ij  }ºä¹ºÓËӈ©äȈ¯Ò¹¯«äººÒº­¯ÈˆÓºº¹Ë¯Ë²ºÈäË΂­ÈÏÒ°ÈäÒ
{g1, g 2 ,..., g n } Ò {g1′ , g 2′ ,..., g n′ } «mã« ˆ°«ˆÈ}ÎË}ºä¹ºÓËӈÈäÒˆËÓϺ¯ºmˆÒ¹È  °Áº¯
ä‚ãÒ¯‚Ëä
       
 |¹¯ËËãËÓÒË            r‚Ëäºmº¯Òˆ ˆºmm˝˰ˆmËÓÓºäãÒÓˮӺ乯º°ˆ¯ÈÓ°ˆmË Λn º¹¯Ë
 ¯              ËãËÓzntovézqwj ( q, p ) T éjorvtzéjkjéqjtzt€pÒ S éjorvkjéqjtz
                         t€p˰ãÒm Λn ÏÈÈÓº­žË}ˆ}ºˆº¯©®m}Èκä­ÈÏҰ˲ȯÈ}ˆË¯Òςˈ°«
                         ‚¹º¯«ºËÓÓ©äÓÈ­º¯ºä n p + q Ò°Ëã ξ i 1i 2...i q  Ë jm ; m = [1, q ] }ºÓ
                                                                                                                     j j ... j
                                                                   1 2      p

                         ˆ¯ÈmȯÒÈӈөË ÒÓË}°© Ò i k ; k = [1, p]   }ºmȯÒÈÓˆÓ©Ë  ÒÏäËÓ« 
                         Ò˰« ¹¯Ò ¹Ë¯Ë²ºË ºˆ ­ÈÏÒ°È {g1 , g 2 ,..., g n }  } ­ÈÏÒ°‚ {g1′ , g 2′ ,..., g n′ }  ¹º
                         ÏÈ}ºÓ‚
                         
                                                                     j1′ j ′ ... j ′                                                 j′
                                                                ξ ′ i1′i2′ 2...i′p q = σ ii11′ σ ii2′2 ...σ i ′pp τ jj11′ τ jj22′ ...τ j qq ξ i1i 22...i p q 
                                                                                                            i                                 j1 j ... j


                         
            
 |¹¯ËËãËÓÒË                Ұ㺠( q + p )  ÓÈÏ©mÈˈ°« kjsntztvxzí                                                                  ÒãÒ éjtmvu  ˆËÓϺ¯È
 ¯
                         ξ   j1 j 2 ... j q i1i 2 ...i p
                                                           
            
 |¹¯ËËãËÓÒË            imȈËÓϺ¯ÈÓÈÏ©mÈ ˆ°«éjkt€uq˰ãÒºÓÒºÓººÒˆººÎˈҹÈÒ
 ¯              mºm°Ë²­ÈÏҰȲÒäË ˆ¯ÈmÓ©Ë}ºä¹ºÓËӈ©
            
            
            
~ÈäËÈÓÒ«° iã« ¯ÈmËÓ°ˆmÈ ˆËÓϺ¯ºm ºÓºº ˆÒ¹È º°ˆÈˆºÓº ˆº­© Ò² }ºä¹ºÓËӈ©
                         ­©ãÒ ¯ÈmÓ© ãÒ  m ÓË}ºˆº¯ºä ­ÈÏÒ°Ë ˆÈ} }È} ÒÏ Áº¯ä‚㠹˯˰ˈÈ
                         }ºä¹ºÓËӈºm °ãË‚ˈ ˆº ªˆÒ ˆËÓϺ¯© ­‚‚ˆ Òäˈ  ¯ÈmÓ©Ë }ºä¹ºÓËӈ©
                         Òmã ­ºä¯‚ºä­ÈÏÒ°Ë
            
                   °p°ãÒ º­žË}ˆ ²È¯È}ˆË¯Òςˈ°« ºÓÒä Ò°ãºä ¹¯ÒËä ÓË ÏÈmÒ°«Òä ºˆ
                        m©­º¯È­ÈÏҰȈºËºäºÎÓº°҈Ȉ ˆËÓϺ¯ºäˆÒ¹È