Аналитическая геометрия и линейная алгебра. Умнов А.Е. - 151 стр.

UptoLike

ВУЗ: 

МФТИ | Москва

Составители: 

Рубрика: 

cÈÏËã



vÒ°Ëä©ãÒÓˮө²¯ÈmÓËÓÒ®
|°È ÏÈ}ãÈËä º ¯ÈÓ äÈ¯Ò© ÓË ¹¯Ëmº°²ºÒ
n
r
 Ò °ã˺mÈËãÓº
¯ÈmËÓmºÓº°Ò
n
r
sººÈ¹º˺¯ËäËºÈÏÒ°ÓºääÒÓº¯Ë}ºº
¯©® ¯È°¹ºãÈÈË°« m ¹º°ãËÓÒ²
r
°¯º}Ȳ ¹Ë¯mÈ« °¯º}È äÈ¯Ò© 
«mã«Ë°«ÓË}ºº¯º®ãÒÓˮӺ®}ºäÒÓÈÒË®º°ÈãÓ©²Ò°ã˺mÈËãÓº ºËË
¯ËËÓÒËºÓº¯ºÓº®°Ò°Ëä©äºÎË©ÏȹҰÈÓºmmÒË
1
...
0
0
...
...
0
...
1
0
...
0
...
0
1
...
...
...
2
1
2
2
2
2
1
2
1
1
2
1
1
1
2
1
2
1
rn
r
rn
rn
rn
rr
n
r
r
r
−
−
−
−
+
+
+++=
ξ
ξ
ξ
λ
ξ
ξ
ξ
λ
ξ
ξ
ξ
λ
ξ
ξ
ξ
ξ
ξ
ξ

Ë
λ
i
inr,[,]
∀= −
1
¹¯ºÒÏmºãÓ©Ë}ºÓ°ÈÓ©
˺¯ËäÈº}ÈÏÈÓÈ

vãË°mÒË

|ËË¯ËËÓÒËÓ˺Ӻ¯ºÓº®°Ò°Ëä©äºÎË©ÈÓºÁº¯
ä㺮
0
0
2
0
1
0
0
2
0
1
2
1
2
2
2
2
1
2
1
1
2
1
1
1
2
1
2
1
...
...
1
...
0
0
...
...
0
...
1
0
...
0
...
0
1
...
...
...
n
r
r
r
rn
r
rn
rn
rn
rr
n
r
r
r
ξ
ξ
ξ
ξ
ξ
ξ
ξ
ξ
λ
ξ
ξ
ξ
λ
ξ
ξ
ξ
λ
ξ
ξ
ξ
ξ
ξ
ξ
+
+
−
−
−
−
+
+
++++=
Ë
0
0
2
0
1
0
0
2
0
1
...
...
n
r
r
r
ξ
ξ
ξ
ξ
ξ
ξ
+
+

«mã«Ë°« ÓË}ºº¯©ä È°Ó©ä ¯ËËÓÒËä Ó˺Ӻ¯ºÓº® °Ò°Ëä©
ÈÒ°ãÈ
],1[, rni
i
−=∀
λ
¹¯ºÒÏmºãÓ©Ë}ºÓ°ÈÓ©
iº}ÈÏÈËã°mº
°
x
0
 ÓË}ºº¯ºË ÓÈ®ËÓÓºË Óȹ¯Òä˯ ¹ºº¯ºä È°ÓºË ¯Ë ËÓÒË
Ó˺Ӻ¯ºÓº® °Ò°Ëä©  È
x
 ËË ¹¯ºÒÏmºãÓºË ¯ËËÓÒË ºÈ ¹º
cÈÏËã
vÒ°ˆËä©ãÒÓˮө²‚¯ÈmÓËÓÒ®



           |ˆ° È ÏÈ}ã ÈËä ˆº ¯ÈÓ äȈ¯Ò© ÓË ¹¯Ëmº°²º҈ nr Ò °ã˺mȈËã Óº
           ¯ÈmËÓmˆºÓº°ˆÒ nrsºˆºÈ¹ºˆËº¯Ëä˺­ÈÏÒ°ÓºääÒÓº¯Ë}ºˆº
           ¯©® ¯È°¹ºãÈÈˈ°« m ¹º°ãËÓÒ² r °ˆ¯º}Ȳ ¹Ë¯mÈ« °ˆ¯º}È äȈ¯Ò©  
           «mã«Ëˆ°« ÓË}ºˆº¯º® ãÒÓˮӺ® }ºä­ÒÓÈÒË® º°ˆÈã Ó©² Ò °ã˺mȈËã Óº º­ËË
           ¯Ë ËÓÒ˺Ӻ¯ºÓº®°Ò°ˆËä©  äºÎˈ­©ˆ ÏȹҰÈÓºmmÒË
           
                                     ξ1           ξ11         ξ12                ξ1n − r
                                     ξ2           ξ 21        ξ 22               ξ 2n − r
                                      ...         ...         ...                   ...
                                     ξr           ξ r1        ξ r2               ξ n−r
                                           = λ1        + λ2        + ... + λn − r r       
                                    ξ r +1         1           0                    0
                                    ξr +2          0           1                    0
                                      ...         ...         ...                   ...
                                     ξn            0           0                     1
           
           Ë λi ,   ∀i = [1, n − r ] ¹¯ºÒÏmºã Ó©Ë}ºÓ°ˆÈӈ©
           
           
        ‘˺¯ËäȺ}ÈÏÈÓÈ
            
            
            
    vãË°ˆmÒË         |­Ë˯ËËÓÒËÓ˺Óº¯ºÓº®°Ò°ˆËä©  äºÎˈ­©ˆ ÈÓºÁº¯
                ä‚㺮
                      
                              ξ1           ξ11         ξ12                ξ1n − r    ξ10              ξ10
                              ξ2           ξ 21        ξ 22               ξ 2n − r   ξ 20             ξ 20
                               ...         ...         ...                   ...      ...              ...
                              ξr                                             n−r
                                           ξ r1        ξr 2
                                                                          ξr         ξr 0
                                                                                                      ξ r0
                                    = λ1        + λ2        + ... +λn − r          + 0 Ë 0 
                             ξ r +1         1           0                    0      ξ r +1           ξ r +1
                             ξr +2          0           1                    0      ξr +2
                                                                                      0
                                                                                                    ξ r0+ 2
                               ...         ...         ...                   ...      ...              ...
                              ξn            0           0                     1      ξ n0             ξ n0
                       
                       «mã«Ëˆ°« ÓË}ºˆº¯©ä È°ˆÓ©ä ¯ËËÓÒËä Ó˺Óº¯ºÓº® °Ò°ˆËä©
                          ÈÒ°ãÈ λi , ∀i = [1, n − r ] ¹¯ºÒÏmºã Ó©Ë}ºÓ°ˆÈӈ©


     iº}ÈÏȈËã°ˆmº
         
           ‚°ˆ  x 0   ÓË}ºˆº¯ºË ÓÈ®ËÓÓºË Óȹ¯Òä˯ ¹º­º¯ºä  È°ˆÓºË ¯Ë ËÓÒË
           Ó˺Óº¯ºÓº® °Ò°ˆËä©   È x   ËË ¹¯ºÒÏmºã ÓºË ¯Ë ËÓÒË ‘ºÈ ¹º

Страницы