Аналитическая геометрия и линейная алгебра. Умнов А.Е. - 36 стр.

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ÙkÓÈã҈ÒË°}È«˺äˈ¯Ò«ÒãÒÓË®ÓÈ«ÈãË­¯ÈµäÓºmkp



                                                      ˆ©­‚‚ˆ°m«ÏÈÓ©°ÙÓºm©äÒµ}È}
                                                                 
                                      →               →
     →                                                                              ξ1 = ξ1′ cos ϕ − ξ 2′ sin ϕ + β1
  e2  e2 ′  e1 ′                                                                  
                                                                                  ξ 2 = ξ1′ sin ϕ + ξ 2′ cos ϕ + β 2
                                                                                       
  O ′                        {¯È°°äºˆ¯ËÓÓºä°ã‚È˺­Ë°Ò°ˆËä©}ºº¯Ò
 
                  →                                              ÓȈäºãÒ­©­©ˆ °ºmä˝ËÓ©¹º°ã˺mȈËã 
     O e1 ϕ                           Ó©ä m©¹ºãÓËÓÒËä ¹È¯ÈããËã Óºº ¹Ë¯ËÓº°È
                                                                       →

                                       Ù°ˆÈ¯º®µ °Ò°ˆËä© ÓÈ mË}ˆº¯ OO′  Ò ¹ºmº¯ºˆÈ
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                                      ~Ë° ¹º°ãË°ºmä˝ËÓÒ«mË}ˆº¯ºm e1 Ò e1′ ˝Ë
                                                      →                                                                                    →
          →
  e 2  e1 ′ 
                                                               ¹ºˆ¯Ë­‚ˈ°« Ï˯}Èã ÓºË ºˆ¯ÈÎËÓÒË mË}ˆº¯È e 2 
                                                               ºˆÓº°ÒˆËã Óº ¹¯«äº® ¹¯º²º«Ë® ˯ËÏ °º
 
                                                               mä˝ËÓÓ©ËmË}ˆº¯©
  O ′                      
 
                                                →              
                  →
     O e1 ϕ e2 ′                 nº¯ä‚㩹˯˲ºÈ­‚‚ˆÒäˈ mÒ
                                                               
 
                                                                                   ξ1 = ξ1′ cos ϕ + ξ 2′ sin ϕ + β1
                                                                                                                        
 èqxytvr                                                   ξ 2 = ξ1′ sin ϕ − ξ 2′ cos ϕ + β 2 .
       
       
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                                                                               →                     →
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              |ˆäˈÒ䈺ã«äȈ¯Ò©¹Ë¯Ë²ºÈ S °m«Ï©mÈ Ë®mȺ¯ˆºÓº¯äÒ¯ºmÈÓÓ©²
­ÈÏÒ°È det S = ±1 ¹¯ÒËä det S = 1 Ë°ãÒº¯ÒËӈÈÒ«‚º­ËÒ²¹È¯­ÈÏÒ°Ó©²mË}ˆº¯ºm
ºÒÓÈ}ºmÈ« ˆºË°ˆ Ë°ãÒºˆ¯ÈÎËÓÒ«Óˈ¯Ë­‚ˈ°« Ò det S = −1 ã«°ã‚È«­ÈÏÒ°Ó©²
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