Аналитическая геометрия и линейная алгебра. Умнов А.Е. - 352 стр.

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                                    → → →            → → →                 → →
                                   ( a , b , c ) = ( a , [ b , c ]) = ξ i [ b , c ]i = ξ i ε ijkη jκ k = ε ijk ξ iη jκ k 
                                                                               
                                                                               
            
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                                 [ a ,[ b , c ]]i = ε ijk ξ j [ b , c ]k = ε ijk ξ j ε klmηlκ m = ε ijk ε klmξ jηlκ m 
                                                                               
            
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                     ε ijk ε klm = δ il δ jm − δ imδ jl ¹¯Ò²ºÒä}¯ÈmËÓ°ˆm‚
                       
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                                          [ a ,[ b , c ]]i = ε ijk ξ j ε klmηlκ m = (δ il δ jm − δ imδ jl )ξ jηlκ m =
                                                                                                                              
                                                                                              → →             → →
                                                           = ηiξ mκ m − κ iξ jη j = ηi ( a , c ) − κ i ( a , b )
                      
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                                                           [ a , [ b , c ]] = b ( a , c ) − c ( a , b )