Аналитическая геометрия и линейная алгебра. Умнов А.Е. - 289 стр.

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                                                                               3

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    α11ξ12 + 2α12ξ1ξ 2 + α 22ξ 22 + 2α13ξ1ξ 3 + α 33ξ 32 + 2α 23ξ 2ξ 3 + 2α14ξ1 + 2α 24ξ 2 + 2α 34ξ 3 + α 44 = 0 
                                                                           
                                3   k
mˆº¯ºº¹º¯«}È              ∑∑ α ik          > 0 
                              k =1 i =1
             
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Á‚Ó}ÒºÓÈã m E 3  ¯ÒmËËä ˺ } ÒȺÓÈã Óºä‚ mÒ‚ º¯ˆººÓÈã Ó©ä º¹Ë¯Èˆº¯ºä ¹º
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                 λ1ξ1′ 2 + λ2ξ 2′ 2 + λ3ξ 3′ 2 + 2α14
                                                   ′ ξ1′ + 2α 24
                                                              ′ ξ 2′ + 2α 34
                                                                          ′ ξ 3′ + α 44
                                                                                     ′ =0,                  λ1 + λ2 + λ3 > 0 
         

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, ¡Ëӈ¯Èã Ó©®°ã‚È® λ λ λ
                            1 2 3 ≠ 0 ÒãÒˆºm°Òよ˺¯Ë䩈ºÎ˰ÈäºË

                                                            α11 α12                α13
                                                        det α 21 α 22              α 23 ≠ 0 
                                                            α 31 α 32              α 33

      º°ãË ¹Ë¯ËÓº°È ÓÈÈãÈ }ºº¯ÒÓȈ ‚°ˆ¯ÈÓ« Ëº ãÒÓˮөË °ãÈÈËä©Ë ¹ºã‚ÈËä
      ‚¯ÈmÓËÓÒË λ1ξ1′′ 2 + λ2ξ 2′′ 2 + λ3ξ 3′′ 2 + α 44
                                                      ′′ = 0  ã« }ºˆº¯ºº äºÎÓº m©Ëã҈  °ãË‚ ÒË
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      ˰ãÒ α ′′44 ≠ 0 
          
             °Îtqu€pëssqwxvql                               ¹¯Ò sgn( λ i ) = sgn(α 44 ′′ ) , i = 1,2,3 
             
             °êssqwxvql                                ¹¯Ò sgn( λ i ) = − sgn(α 44
                                                                                             ′′ ) , i = 1,2,3 
             
             °Ìltvwvsvxzt€pmqwnéivsvql
                                                   ¹¯Ò sgn( λ1 ) = sgn( λ2 ) = − sgn( λ3 ) = − sgn(α 44 ′′ )