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orthogonal_complement

? orthogonal_complement;

2067;

Calculate

orthogonal_complement

? orthogonal_complement;

Calculate

orthogonal_complement

? orthogonal_complement;

2067;

Calculate

orthogonal_complement

? orthogonal_complement;

Calculate

orthogonal_complement

Run Example
(%i1)load  (eigen);
(%o1)           /usr/share/maxima/5.21.1/share/matrix/eigen.mac
(%i2) a  :  covect  ([1,  2,  3]);
                                     [ 1 ]
                                     [   ]
(%o2)                                [ 2 ]
                                     [   ]
                                     [ 3 ]
(%i3) b  :  covect  ([2,  1,  2]);
                                     [ 2 ]
                                     [   ]
(%o3)                                [ 1 ]
                                     [   ]
                                     [ 2 ]
(%i4) print  ("a  =  ",  a,  "  b  =  ",  b);
       [ 1 ]          [ 2 ]
       [   ]          [   ]
a  =   [ 2 ]   b  =   [ 1 ] 
       [   ]          [   ]
       [ 3 ]          [ 2 ]
                                     [ 2 ]
                                     [   ]
(%o4)                                [ 1 ]
                                     [   ]
                                     [ 2 ]
(%i5) basis  :  orthogonal_complement  (a,  b);
                                      [  1  ]
                                      [     ]
(%o5)                            span([  4  ])
                                      [     ]
                                      [ - 3 ]
(%i6) first  (basis);
                                    [  1  ]
                                    [     ]
(%o6)                               [  4  ]
                                    [     ]
                                    [ - 3 ]
(%i7) 
Run Example
load  (eigen);
(%o1)           /usr/share/maxima/5.21.1/share/matrix/eigen.mac
(%i2) a  :  covect  ([1,  1,  0]);
                                     [ 1 ]
                                     [   ]
(%o2)                                [ 1 ]
                                     [   ]
                                     [ 0 ]
(%i3) b  :  covect  ([1,  0,  0]);
                                     [ 1 ]
                                     [   ]
(%o3)                                [ 0 ]
                                     [   ]
                                     [ 0 ]
(%i4) print  ("a  =  ",  a,  "  b  =  ",  b);
       [ 1 ]          [ 1 ]
       [   ]          [   ]
a  =   [ 1 ]   b  =   [ 0 ] 
       [   ]          [   ]
       [ 0 ]          [ 0 ]
                                     [ 1 ]
                                     [   ]
(%o4)                                [ 0 ]
                                     [   ]
                                     [ 0 ]
(%i5) basis  :  orthogonal_complement  (a,  b);
                                       [ 0 ]
                                       [   ]
(%o5)                             span([ 0 ])
                                       [   ]
                                       [ 1 ]
(%i6) first  (basis);
                                     [ 0 ]
                                     [   ]
(%o6)                                [ 0 ]
                                     [   ]
                                     [ 1 ]
(%i7) 
Run Example
load (vector_rebuild);
(%o1)      /usr/share/maxima/5.21.1/share/vector/vector_rebuild.mac
(%i2) powerdisp : true;
(%o2)                                true
(%i3) v([args]) := covect(args);
(%o3)                      v([args]) := covect(args)
(%i4) a : v(1,2,3);
                                     [ 1 ]
                                     [   ]
(%o4)                                [ 2 ]
                                     [   ]
                                     [ 3 ]
(%i5) n : v(2, 25, 10);
                                    [ 2  ]
                                    [    ]
(%o5)                               [ 25 ]
                                    [    ]
                                    [ 10 ]
(%i6) oc : orthogonal_complement(n);
                                [ - 25 ]  [  0   ]
                                [      ]  [      ]
(%o6)                      span([  2   ], [  10  ])
                                [      ]  [      ]
                                [  0   ]  [ - 25 ]
(%i7) [b, c] : [first(oc), second(oc)];
                              [ - 25 ]  [  0   ]
                              [      ]  [      ]
(%o7)                        [[  2   ], [  10  ]]
                              [      ]  [      ]
                              [  0   ]  [ - 25 ]
(%i8) x : a + r * b + s * c;
                        [ 1 ]     [ - 25 ]     [  0   ]
                        [   ]     [      ]     [      ]
(%o8)                   [ 2 ] + r [  2   ] + s [  10  ]
                        [   ]     [      ]     [      ]
                        [ 3 ]     [  0   ]     [ - 25 ]
(%i9) 

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