Аналитическая геометрия и линейная алгебра. Умнов А.Е. - 167 стр.

UptoLike

Составители: 

Рубрика: 

cÈÏ Ëã
171
ÒÓˮӺË¹¯º°¯ÈÓ°mº
∑∑
======
=
=
==
n
i
i
n
j
jij
n
i
iij
n
j
jj
n
j
ji
n
i
i
gggxg
111111
)(
ξ
σσ
ξ
ξ
ξ

ÒãÒ
og
i
n
i
n
j
jiji
=
∑∑
==
11
)(
ξ
σ
ξ
sº˰ãÒãÒÓË®ÓÈ«}ºäÒÓÈÒ«ãÒÓˮӺÓËÏÈmÒ°Ò䩲
ªãËäËÓºm¯ÈmÓÈÓãËmºäªãËäËÓººÓÈ¯ÒmÒÈãÓÈ«|}È¹ºãÈËäº
],1[;
1
ni
n
j
jiji
=
=
=
ξ
σ
ξ

˺¯ËäÈº}ÈÏÈÓÈ

jÓÈË ºmº¯« ˰ãÒ ªãËäËÓ© ÙÓºmººµ ÈÏÒ°È m©¯ÈÎÈ°« ˯ËÏ ªãËäËÓ© Ù°ȯººµ
¹¯Ò ¹ºäºÒ ¯ÈÓ°¹ºÓÒ¯ºmÈÓÓº® äÈ¯Ò© ¹Ë¯Ë²ºÈ
S
7
 º }ºº¯ÒÓÈÓ©® °ºãËm
Ù°ȯºäµ ÈÏÒ°Ë ¯ÈmËÓ ¹¯ºÒÏmËËÓÒ äÈ¯Ò© ¹Ë¯Ë²ºÈ ÓÈ }ºº¯ÒÓÈÓ©® °ºãËm
ÙÓºmºäµÈÏÒ°Ë{äÈ¯ÒÓº®Áº¯äË˰ãÒ
=
g
g
g
S
g
g
g
nn
1
2
1
2
... ...
T
º
nn
S
ξ
ξ
ξ
ξ
ξ
ξ
=
......
2
1
2
1

ºäÓºÎ˰mÈãÒÓˮӺº¹¯º°¯ÈÓ°mÈ
º¹¯º°¯ÈÓ°mº
|¹¯ËËãËÓÒË

s˹°ºË äÓºÎ˰mº
 º¯ÈϺmÈÓÓºË ÒÏ ªãËäËÓºm ãÒÓˮӺº ¹¯º
°¯ÈÓ°mÈ
Λ
 ÓÈÏ©mÈË°« wvlwévxzéjtxzkvuªºº ãÒÓˮӺº ¹¯º
°¯ÈÓ°mÈ˰ãÒã«ã©²
yx,
ÒãººÒ°ãÈ
λ

°

+ yx
°

x
λ
~ÈäËÈÓÒË
jÏº¹¯ËËãËÓÒ«°ãËËºäÓºÎ˰mº
°Èäº«mã«Ë°«ãÒÓË®
Ó©ä¹¯º°¯ÈÓ°mºä¹º°}ºã}ã«Ó˺ºËmÒÓºm©¹ºãÓ«°«m°ËÈ}
°Òºä©º¹Ë¯ÈÒ®mãÒÓˮӺä¹¯º°¯ÈÓ°mË
c È Ï  Ë ã                                                      171
ÒÓˮӺ˹¯º°ˆ¯ÈÓ°ˆmº



                                                    n                           n                     n            n                     n      n
                                                  ∑ξ i g i = x = ∑ξ ′j g ′j = ∑ξ ′j ∑σ ij g i = ∑ ( ∑σ ijξ ′j ) g i 
                                                  i =1                         j =1                  j =1         i =1                i =1 j =1
               
                            n               n
               ÒãÒ       ∑ (ξ i − ∑σ ijξ ′j )g i = o sº˰ãÒãÒÓË®ÓÈ«}ºä­ÒÓÈÒ«ãÒÓˮӺÓËÏÈmÒ°Ò䩲
                          i =1             j =1
               ªãËäËӈºm¯ÈmÓÈӂãËmºä‚ªãËäËӈ‚ˆººÓȈ¯ÒmÒÈã ÓÈ«|ˆ}‚ȹºã‚ÈË䈺
                                                                                             n
                                                                                 ξ i = ∑σ ijξ ′j ;                     ∀i = [1, n] 
                                                                                           j =1
                                                                                                              
       ‘˺¯ËäȺ}ÈÏÈÓÈ



jÓÈË ºmº¯« ˰ãÒ ªãËäËӈ© ÙÓºmººµ ­ÈÏÒ°È m©¯ÈÎÈ ˆ°« ˯ËÏ ªãËäËӈ© Ù°ˆÈ¯ººµ
                                                                                                                                     7
¹¯Ò ¹ºäºÒ ˆ¯ÈÓ°¹ºÓÒ¯ºmÈÓÓº® äȈ¯Ò© ¹Ë¯Ë²ºÈ S  ˆº }ºº¯ÒÓȈө® °ˆºã­Ë m
Ù°ˆÈ¯ºäµ ­ÈÏÒ°Ë ¯ÈmËÓ ¹¯ºÒÏmËËÓÒ  äȈ¯Ò© ¹Ë¯Ë²ºÈ ÓÈ }ºº¯ÒÓȈө® °ˆºã­Ë m
                                                                                                       g1′                          g1        ξ1      ξ1′
                                                                                                       g 2′                 T       g2        ξ2      ξ 2′
ÙÓºmºäµ­ÈÏÒ°Ë{äȈ¯ÒÓº®Áº¯äË˰ãÒ                                                                          = S                   ˆº     = S      
                                                                                                       ...                          ...       ...     ...
                                                                                                       g n′                         gn        ξn      ξ n′
                   
                   
                   
                   
ºäÓºÎ˰ˆmÈãÒÓˮӺº¹¯º°ˆ¯ÈÓ°ˆmÈ
                   
                   
                   
º¹¯º°ˆ¯ÈÓ°ˆmº
                   
                   
    |¹¯ËËãËÓÒË                   s˹‚°ˆºË äÓºÎ˰ˆmº Ω  º­¯ÈϺmÈÓÓºË ÒÏ ªãËäËӈºm ãÒÓˮӺº ¹¯º
                            °ˆ¯ÈÓ°ˆmÈ Λ  ÓÈÏ©mÈˈ°« wvlwévxzéjtxzkvu ªˆºº ãÒÓˮӺº ¹¯º
                                   °ˆ¯ÈÓ°ˆmÈ˰ãÒã«ã ­©² x, y ∈ Ω Òã ­ººÒ°ãÈλ
                                                                ° x + y ∈ Ω 
                                                                                                          ° λx ∈ Ω 
                   
                   
                   
 ~ÈäËÈÓÒË                      jϺ¹¯ËËãËÓÒ«°ãË‚ˈˆºäÓºÎ˰ˆmº Ω °È享mã«Ëˆ°«ãÒÓË®
                                  ө乯º°ˆ¯ÈÓ°ˆmºä¹º°}ºã }‚ã«Ó˺ºËmÒÓºm©¹ºãÓ« ˆ°«m°ËÈ}
                                  °Òºä©º¹Ë¯ÈÒ®mãÒÓˮӺ乯º°ˆ¯ÈÓ°ˆmË