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columnspace-matrix

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

columnspace(m);

Calculate

columnspace-matrix

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

columnspace(m);

Calculate

columnspace

? columnspace;

Calculate

columnspace-matrix

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

columnspace(m);

Calculate

columnspace-matrix

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

columnspace(m);

Calculate

columnspace-matrix

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

columnspace(m);

Calculate

columnspace-matrix

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

columnspace(m);

Calculate

columnspace-matrix

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

columnspace(m);

Calculate

columnspace-matrix-nullspace-transpose

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

nullspace(m);

a:transpose(m);

Calculate

columnspace-matrix

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

columnspace(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
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) 
Run Example
? columnspace;

 -- Function: columnspace (<M>)
     If <M> is a matrix, return `span (v_1, ..., v_n)', where the set
     `{v_1, ..., v_n}' is a basis for the column space of <M>.  The span
     of the empty set is `{0}'. Thus, when the column space has only
     one member, return `span ()'.


(%o1)                                true
(%i2) 

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Help for Columnspace