(%i2) "Spiegelung an der x-Achse S_x"$

(%i3) S_x: matrix([1.0,0.0],[0.0,-1.0]);
                                [ 1.0   0.0  ]
(%o3)                           [            ]
                                [ 0.0  - 1.0 ]

(%i4) determinant(S_x);
(%o4)                                - 1.0

(%i5) "Spiegelung an der y-Achse S_y"$

(%i6) S_y: matrix([-1.0,0.0],[0.0,1.0]);
                                [ - 1.0  0.0 ]
(%o6)                           [            ]
                                [  0.0   1.0 ]

(%i7) determinant(S_y);
(%o7)                                - 1.0

(%i8) "Streckung um den Faktor 2 T_2"$

(%i9) T_2: matrix([2.0,0.0],[0.0,2.0]);
                                 [ 2.0  0.0 ]
(%o9)                            [          ]
                                 [ 0.0  2.0 ]

(%i10) determinant(T_2);
(%o10)                                4.0

(%i11) "Scherung in x-Richtung um 0.5 LE U"$

(%i12) U: matrix([1.0,0.5],[0.0,1.0]);
                                 [ 1.0  0.5 ]
(%o12)                           [          ]
                                 [ 0.0  1.0 ]

(%i13) determinant(U);
(%o13)                                1.0

(%i14) "Projektionsmatrix P_x"$

(%i15) P_x: matrix([1.0,0.0],[0.0,0.0]);
                                 [ 1.0  0.0 ]
(%o15)                           [          ]
                                 [ 0.0  0.0 ]

(%i16) determinant(P_x);
(%o16)                                0.0

(%i17) "Projektionsmatrix P_y"$

(%i18) P_y: matrix([0.0,0.0],[0.0,1.0]);
                                 [ 0.0  0.0 ]
(%o18)                           [          ]
                                 [ 0.0  1.0 ]

(%i19) determinant(P_y);
(%o19)                                0.0

(%i20) "Drehmatrix D_90"$

(%i21) D_90: matrix([0.0,-1.0],[1.0,0.0]);
                                [ 0.0  - 1.0 ]
(%o21)                          [            ]
                                [ 1.0   0.0  ]

(%i22) determinant(D_90);
(%o22)                                1.0

(%i23) "Drehmatrix D_180"$

(%i24) D_180: matrix([-1.0,0.0],[0.0,-1.0]);
                               [ - 1.0   0.0  ]
(%o24)                         [              ]
                               [  0.0   - 1.0 ]

(%i25) determinant(D_180);
(%o25)                                1.0

(%i26) "Drehmatrix D_45"$

(%i27) D_45: matrix([0.5*sqrt(2),-0.5*sqrt(2)],[0.5*sqrt(2),0.5*sqrt(2)]);
                        [ 0.5 sqrt(2)  - 0.5 sqrt(2) ]
(%o27)                  [                            ]
                        [ 0.5 sqrt(2)   0.5 sqrt(2)  ]

(%i28) determinant(D_45);
(%o28)                                1.0

(%i29) D_45 . D_45 = D_90
                                [ 0.0  - 1.0 ]
(%o29)                          [            ]
                                [ 1.0   0.0  ]

(%i30) D_90 . D_90 = D_180
                               [ - 1.0   0.0  ]
(%o30)                         [              ]
                               [  0.0   - 1.0 ]

(%i31) D_180 . D_180 = E (Einheitsmatrix)
                                 [ 1.0  0.0 ]
(%o31)                           [          ]
                                 [ 0.0  1.0 ]

(%i32) "allgemeine Drehmatrix"$

(%i33) D_all: matrix([cos(a),-sin(a)],[sin(a),cos(a)]);
                             [ cos(a)  - sin(a) ]
(%o33)                       [                  ]
                             [ sin(a)   cos(a)  ]