Аналитическая геометрия и линейная алгебра. Умнов А.Е. - 111 стр.

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                                        α11 α12                                                α11 α12                        α11 α12
                                                               ( xy            x2                                    x1                   x2
                          →    →
                      A (r1 + r2 ) =                                      +           )=                                 +                    =
                                                                       1

                                        α 21 α 22                      1       y2              α 21 α 22             y1       α 21 α 22   y2       
                                        →            →
                                       + Ar
                                    = Ar                  .
                                        1   2
          
                                        →           α11 α12                λx    α11 α12                    x             →
          kÓÈãºÒÓº A ( λ r ) =                                            =λ                                 = λ A r 
                                                    α 21 α 22              λy    α 21 α 22                  y
      
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                                                                       →       →           →        →              → →
                                                         ° A ( r1 + r2 ) = A r1 + A r2 ,                  ∀ r1 , r2 
                                                                           →               →            →
                                                         ° A ( λ r ) = λ A r              , ∀ r , λ 
                          
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                      →        →            →            →                 →           →
          ‚°ˆ  r = x g1 + y g 2 Ò A r = x ∗ g1 + y ∗ g 2 ˆºÈ
          
                                                    →           →                   →          →                 →            →
                                            x ∗ g1 + y ∗ g 2 = A ( x g1 + y g 2 ) = x A g1 + y A g 2 
          
          
                                   →                →              →               →            →                →
          |­ºÏÓÈÈ« A g1 = α11 g1 + α 21 g 2 Ò A g 2 = α12 g1 + α 22 g 2 ¹ºã‚Òä
          
                                →               →              →               →                                 →                        →
                           x ∗ g1 + y ∗ g 2 = x A g1 + y A g 2 = (α11 x + α12 y ) g1 + (α 21 x + α 22 y ) g 2 
          
                                  x ∗ = α11 x + α12 y         x∗    α11 α12                                                              x
          |}ºÓȈËã Óº¹ºã‚ÈËä  ∗                   ÒãÒ     =                                                                        
                                  y = α 21 x + α 22 y         y ∗
                                                                     α 21 α 22                                                        g
                                                                                                                                          y
      
      
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