Аналитическая геометрия и линейная алгебра. Умнов А.Е. - 123 стр.

UptoLike

ВУЗ: 

МФТИ | Москва

Составители: 

Рубрика: 

cÈÏËã

¯Ëº¯ÈϺmÈÓÒ«¹ãº°}º°Ò
sÈ}ºÓËË°ãÒ
0≠U
º
ºÓºËÓÒË}ºº¯ÒÓÈmË}º¯ºm
p
∗
→
Ò
q
∗
→
ÓȲº
Ò°«ÒÏ}mȯÈÓºº¯ÈmÓËÓÒ«
01
2
)()(
2
=−−
η
ξ
η
ξ
U
V
ÒäË˺Ë®°mÒ
ËãÓ©Ë¯ËËÓÒ«
()
,
ξ
η
12
2
2
1=± +
V
U
V
U
¹¯ÒãºäÓËÓãËmºä
U

˺¯ËäÈº}ÈÏÈÓÈ

|¯ººÓÈãÓ©Ë¹¯Ëº¯ÈϺmÈÓÒ«¹ãº°}º°Ò
|¹¯ËËãËÓÒË

Ìézvmvtjstu wénviéjovkjtqnu ¹ãº°}º°Ò
P
ÓÈÏ©mÈË°« ãÒÓˮө®
º¹Ë¯Èº¯
Q
mÒÈ
x
y
Q
x
y
e
*
*
=+
β
β
1
2
 äÈ¯ÒÈ }ºº¯ºº
Q
e
=
ωω
ωω
11 12
21 22
º¯ººÓÈãÓÈ« m ãº® º¯ºÓº¯äÒ¯ºmÈÓÓº® °Ò°ËäË
}ºº¯ÒÓÈ
sȹºäÓÒä º ¹º º¹¯ËËãËÓÒ  äÈ¯ÒÈ
Q
ÓÈÏ©mÈË°« º¯ººÓÈãÓº®
Ë°ãÒ
QQ
−
=
1T

~ÈäËÒäºº¯ººÓÈãÓºË¹¯Ëº¯ÈϺmÈÓÒË«mã«Ë°«È°Ó©ä°ãÈËäÈÁÁÒÓ
Óºº ¹¯Ëº¯ÈϺmÈÓÒ« ¹º°}ºã} m °Òã ˺¯Ëä©  ÒäËË äË°º ãÒº
det
Q
e
=
1

ãÒº
det
Q
e
=−
1
 ºäÒäº ¹¯ÒmËËÓÓ©² m ¹ ÈÁÁÒÓÓ©² °mº®°m º¯ººÓÈãÓ©Ë
¹¯Ëº¯ÈϺmÈÓÒ«ºãÈÈ°mºÒäÒ°¹ËÒÁÒË°}ÒäÒº°ºËÓÓº°«äÒcÈ°°äº¯Òäº°Óºm
Ó©ËÒÏÓÒ²
¯ÒÏÓÈ}ºººÓË}ºº¯©®ãÒÓˮө®º¹Ë¯Èº¯«mã«Ë°«º¯ººÓÈãÓ©ääº
ÎË©°Áº¯äãÒ¯ºmÈÓ}È}
˺¯ËäÈ

ÒÓˮө® º¹Ë¯Èº¯ ÓÈ ¹ãº°}º°Ò «mã«Ë°« º¯ººÓÈãÓ©ä Ë°ãÒ ˺
äÈ¯ÒÈº¯ººÓÈãÓÈ«²º«©mºÓº®º¯ºÓº¯äÒ¯ºmÈÓÓº®°Ò°ËäË
}ºº¯ÒÓÈ
iº}ÈÏÈËã°mº
iã«º}ÈÏÈËã°mÈº°ÈºÓºËÒ°«ºº¯ººÓÈãÓº°äÈ¯Ò©ãÒÓË®
Óººº¹Ë¯Èº¯È°º²¯ÈÓ«Ë°«¹¯Ò¹Ë¯Ë²ºËººÓººº¯ºÓº¯äÒ¯ºmÈÓÓººÈÏÒ°È
ÓÈ¹ãº°}º°Ò}¯ºä
cÈÏËã
¯Ëº­¯ÈϺmÈÓÒ«¹ãº°}º°ˆÒ



                                                                                                                      →          →
                  sÈ}ºÓËË°ãÒ U ≠ 0 ˆº ºˆÓº ËÓÒË}ºº¯ÒÓȈmË}ˆº¯ºm p ∗ Ò q ∗ ÓȲº
                                                                             ξ            2V ξ
                      ҈°«ÒÏ}mȯȈӺº‚¯ÈmÓËÓÒ«                      (η )   2
                                                                                      −     ( ) − 1 = 0 ÒäË ËºË®°ˆmÒ
                                                                                          U η
                                                    ξ        V   V2
                      ˆËã Ó©Ë¯Ë ËÓÒ«            ( η ) 1,2 U U 2 + 1 ¹¯Òã ­ºäÓËӂãËmºäU
                                                           =   ±
      
      ‘˺¯ËäȺ}ÈÏÈÓÈ
             
             
             
             
|¯ˆººÓÈã ө˹¯Ëº­¯ÈϺmÈÓÒ«¹ãº°}º°ˆÒ
             
             
             
    |¹¯ËËãËÓÒË            Ìézvmvtjst€u wénviéjovkjtqnu ¹ãº°}º°ˆÒ P ÓÈÏ©mÈˈ°« ãÒÓˮө®
    
                                                                        x*                    x   β1
                            º¹Ë¯Èˆº¯         Q       mÒÈ              = Q                 +            äȈ¯ÒÈ            }ºˆº¯ºº
                                                                        y*                e   y   β2
                                          ω11 ω12
                             Q       =            º¯ˆººÓÈã ÓÈ« m ã ­º® º¯ˆºÓº¯äÒ¯ºmÈÓÓº® °Ò°ˆËäË
                                  e       ω21 ω22
                            }ºº¯ÒÓȈ
             
             sȹºäÓÒä ˆº ¹º º¹¯ËËãËÓÒ   äȈ¯ÒÈ Q  ÓÈÏ©mÈˈ°« º¯ˆººÓÈã Óº®
                 −1          T
Ë°ãÒ Q               = Q 
       
             

             ~ÈäˈÒ䈺º¯ˆººÓÈã Ӻ˹¯Ëº­¯ÈϺmÈÓÒË«mã«Ëˆ°«È°ˆÓ©ä°ã‚ÈËäÈÁÁÒÓ
Óºº ¹¯Ëº­¯ÈϺmÈÓÒ« ¹º°}ºã }‚ m °Òã‚ ˆËº¯Ëä©  ÒäËˈ äË°ˆº ãÒ­º det Q                                                   e
                                                                                                                                               = 1 
ãÒ­º det Q           e
                           = −1  ºäÒäº ¹¯ÒmËËÓÓ©² m ¹ ÈÁÁÒÓÓ©² °mº®°ˆm º¯ˆººÓÈã Ó©Ë
¹¯Ëº­¯ÈϺmÈÓÒ«º­ãÈÈ ˆ°mºÒäÒ°¹ËÒÁÒË°}ÒäÒº°º­ËÓÓº°ˆ«äÒcÈ°°äºˆ¯Ò亰Ӻm
Ó©ËÒÏÓÒ²
           
           ¯ÒÏÓÈ}ˆººˆºÓË}ºˆº¯©®ãÒÓˮө®º¹Ë¯Èˆº¯«mã«Ëˆ°«º¯ˆººÓÈã Ó©ääº
Îˈ­©ˆ °Áº¯ä‚ãÒ¯ºmÈÓ}È}
           
           
 ‘˺¯ËäÈ        ÒÓˮө® º¹Ë¯Èˆº¯ ÓÈ ¹ãº°}º°ˆÒ «mã«Ëˆ°« º¯ˆººÓÈã Ó©ä Ë°ãÒ Ëº
          äȈ¯ÒȺ¯ˆººÓÈã ÓÈ«²ºˆ«­©mºÓº®º¯ˆºÓº¯äÒ¯ºmÈÓÓº®°Ò°ˆËäË
                 }ºº¯ÒÓȈ
           
  iº}ÈÏȈËã°ˆmº
         
         i㫺}ÈÏȈËã °ˆmȺ°ˆÈˆºÓº‚­Ë҈ °«ˆºº¯ˆººÓÈã Óº°ˆ äȈ¯Ò©ãÒÓË®
         Óººº¹Ë¯Èˆº¯È°º²¯Èӫˈ°«¹¯Ò¹Ë¯Ë²ºËºˆºÓººº¯ˆºÓº¯äÒ¯ºmÈÓÓºº­ÈÏÒ°È
         Óȹ㺰}º°ˆÒ}¯‚ºä‚

Страницы