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columnspace-matrix

m:matrix([1,1],[-1,-1]);

columnspace(m);

Calculate

columnspace-matrix

m:matrix([9,5,-4,2],[...

columnspace(m);

Calculate

columnspace-matrix

m:matrix([1,2,5,-3],[...

columnspace(m);

Calculate

columnspace-matrix-triangularize

A:matrix([7,0,1,3,2],...

B:triangularize(A);

columnspace(B);

Calculate

columnspace-matrix-transpose-triangularize

A:matrix([7,0,1,3,2],...

B:transpose(A);

c:triangularize(B);

Calculate

columnspace-matrix-nullspace

m:matrix([15,9,-3,9],...

nullspace(m);

columnspace(m);

Calculate

columnspace

? columnspace;

Calculate

columnspace-matrix

m:matrix([1,2,3],[2,5...

columnspace(m);

Calculate

columnspace-matrix-transpose

A:matrix([7,0,1,3,2],...

B:transpose(A);

columnspace(B);

Calculate

columnspace-matrix-nullspace-transpose

m:matrix([1,-1,2],[2,...

nullspace(m);

a:transpose(m);

Calculate

columnspace

Run Example
(%i1)m:matrix([1,-1,2],[2,0,2],[1,3,-2],[1,4,-3]);
                                [ 1  - 1   2  ]
                                [             ]
                                [ 2   0    2  ]
(%o1)                           [             ]
                                [ 1   3   - 2 ]
                                [             ]
                                [ 1   4   - 3 ]
(%i2) nullspace(m);
                                      [  2  ]
                                      [     ]
(%o2)                            span([ - 2 ])
                                      [     ]
                                      [ - 2 ]
(%i3) a:transpose(m);
                             [  1   2   1    1  ]
                             [                  ]
(%o3)                        [ - 1  0   3    4  ]
                             [                  ]
                             [  2   2  - 2  - 3 ]
(%i4) columnspace(transpose(a));
                                  [ - 1 ]  [ 1 ]
                                  [     ]  [   ]
                                  [  0  ]  [ 2 ]
(%o4)                        span([     ], [   ])
                                  [  3  ]  [ 1 ]
                                  [     ]  [   ]
                                  [  4  ]  [ 1 ]
(%i5) 
Run Example
A:matrix([7,0,1,3,2],[8,9,3,7,0],[1,3,2,8,9]);
                               [ 7  0  1  3  2 ]
                               [               ]
(%o1)                          [ 8  9  3  7  0 ]
                               [               ]
                               [ 1  3  2  8  9 ]
(%i2) B:transpose(A);
                                  [ 7  8  1 ]
                                  [         ]
                                  [ 0  9  3 ]
                                  [         ]
(%o2)                             [ 1  3  2 ]
                                  [         ]
                                  [ 3  7  8 ]
                                  [         ]
                                  [ 2  0  9 ]
(%i3) columnspace(B);
                                [ 1 ]  [ 7 ]  [ 8 ]
                                [   ]  [   ]  [   ]
                                [ 3 ]  [ 0 ]  [ 9 ]
                                [   ]  [   ]  [   ]
(%o3)                      span([ 2 ], [ 1 ], [ 3 ])
                                [   ]  [   ]  [   ]
                                [ 8 ]  [ 3 ]  [ 7 ]
                                [   ]  [   ]  [   ]
                                [ 9 ]  [ 2 ]  [ 0 ]
(%i4) 
Run Example
m:matrix([1,2,3],[2,5,8],[2,1,0]);
                                  [ 1  2  3 ]
                                  [         ]
(%o1)                             [ 2  5  8 ]
                                  [         ]
                                  [ 2  1  0 ]
(%i2) columnspace(m);
                                   [ 1 ]  [ 2 ]
                                   [   ]  [   ]
(%o2)                         span([ 2 ], [ 5 ])
                                   [   ]  [   ]
                                   [ 2 ]  [ 1 ]
(%i3) 

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