Аналитическая геометрия и линейная алгебра. Умнов А.Е. - 206 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
° sÈ®Ëä˹˯°º°mËÓÓ©ËmË}º¯©°
λλ
==
1
1
ºÈ
−−
−−
−−
=
222
222
322
0
0
0
1
2
3
ξ
ξ
ξ

¯Ëº¯ÈϺmÈmäÈ¯Ò¹º°¯ºËÓÓº®°Ò°Ëä©ãÒÓˮө²¯ÈmÓËÓÒ®¹ºãÒä}ºä¹º
ÓËÓ©°º°mËÓÓ©²mË}º¯ºm
21
,
ξξ
Ò
3
ξ
ÒÏ°ãºmÒ®
0
0
0
001
111
3
2
1
=
ξ
ξ
ξ
vã˺
mÈËãÓº°º°mËÓÓ©®mË}º¯
f
1
ºmËÈÒ®°º°mËÓÓºäÏÓÈËÓÒ
λ
1
1
=
ÒäËË
0;
1
1
0
3
2
1
=
µµ
ξ
ξ

° °˹˯
λλ
==
2
i
ºÈ°Ò°ËäãÒÓˮө²¯ÈmÓËÓÒ®
0
0
0
323
212
221
3
2
1
=
ξ
ξ
ξ
i
i
i
äºÎÓº¹¯º°Ò¯ÈÏËãÒm
ºËȰÒ¹Ë¯mºº¯ÈmÓËÓÒ«ÓÈ
1
+
i
~ÈäËÒäºm
¹ºãËÓÓº®È}Òäº¯ÈϺä°Ò°ËäË
0
0
0
323
212
111
3
2
1
=
+
ξ
ξ
ξ
i
i
ii
¯ËË¯ÈmÓËÓÒËº}ÈÏ©mÈË°«°ä亮¹Ë¯m©²m²Ò˺äºÎÓºº¯º°Ò}È}ãÒ
ÓˮӺÏÈmÒ°ÒäºË
~ÈäËÓÒmÏÈËämº¯ºË¯ÈmÓËÓÒË¯ÈÏÓº°mºËÓÓºº¹Ë¯mººÒmº¯ºº¹ºãÒä
0
0
0
2310
111
3
2
1
=
+
+
ξ
ξ
ξ
ii
ii


¯ÈmÒãºËãËÓÒ«}ºä¹ãË}°Ó©²Ò°Ëã¹¯ÒmËËÓºm¯ÒãºÎËÓÒÒ
 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



° sÈ®ËäˆË¹Ë¯ °º­°ˆmËÓÓ©ËmË}ˆº¯©‚°ˆ  λ = λ1 = 1 ˆºÈ
    
                                                           −2 −2 2               ξ1   0
                                                           −2 −2 2               ξ2 = 0 
                                                           −3 −2 2               ξ3   0
     
     ¯Ëº­¯ÈϺmÈmäȈ¯Ò‚¹º°ˆ¯ºËÓÓº®°Ò°ˆËä©ãÒÓˮө²‚¯ÈmÓËÓÒ®¹ºã‚Òä}ºä¹º
                                                                      ξ1    0
                                                              1                                      1     −1
     ÓËӈ©°º­°ˆmËÓÓ©²mË}ˆº¯ºm ξ1 ,ξ 2 Ò ξ 3 ÒÏ‚°ãºmÒ®         ξ 2 = 0 vã˺
                                                              1   0                                  0
                                                                      ξ3    0
     mȈËã Óº°º­°ˆmËÓÓ©®mË}ˆº¯ f 1 ºˆmËÈ Ò®°º­°ˆmËÓÓºä‚ÏÓÈËÓÒ  λ1 = 1 ÒäËˈ
     mÒ
     
                                                            ξ1      0
                                                            ξ 2 = µ 1 ; ∀µ ≠ 0 
                                                            ξ3      1
    
    
° ‚°ˆ ˆË¹Ë¯  λ = λ2 = i ˆºÈ°Ò°ˆËä‚ãÒÓˮө²‚¯ÈmÓËÓÒ®  
    
                                                     −1− i − 2               2       ξ1   0
                                                      − 2 −1− i              2       ξ2 = 0 
                                                       −3         −2        3−i      ξ3   0
     
     äºÎÓº‚¹¯º°ˆÒˆ ¯ÈÏËãÒm  º­ËȰˆÒ¹Ë¯mºº‚¯ÈmÓËÓÒ«ÓÈ 1 + i ~ÈäˈÒ䈺m
     ¹ºã‚ËÓÓº®ˆÈ}Ò亭¯ÈϺä°Ò°ˆËäË
     
                                                       − 1 − 1+ i 1− i              ξ1   0
                                                       − 2 −1− i   2                ξ2 = 0 
                                                       − 3 − 2 3−i                  ξ3   0
     
     ˆ¯Ëˆ Ë‚¯ÈmÓËÓÒ˺}ÈÏ©mÈˈ°«°‚ä亮¹Ë¯m©²m‚²Ò˺äºÎÓººˆ­¯º°Òˆ }È}ãÒ
     ÓˮӺÏÈmÒ°ÒäºË
     
     
     ~ÈäËÓÒmÏȈËämˆº¯ºË‚¯ÈmÓËÓÒ˯ÈÏÓº°ˆ ‚mºËÓÓºº¹Ë¯mººÒmˆº¯ºº¹ºã‚Òä
     
                                                                                   ξ1    0
                                                      −1      − 1+ i  1− i
                                                                                   ξ 2 = 0 
                                                       0     − 1 + 3i 2i
                                                                                   ξ3    0
     


   ¯ÈmÒãºËãËÓÒ«}ºä¹ãË}°Ó©²Ò°Ë㹯ÒmËËÓºm¯ÒãºÎËÓÒÒ