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invert_by_lu

? invert_by_lu;

Calculate

invert_by_lu

? invert_by_lu;

Calculate

invert_by_lu

Run Example
(%i1)a:matrix([1,2],[3,4]);
                                   [ 1  2 ]
(%o1)                              [      ]
                                   [ 3  4 ]
(%i2) b:matrix([5,6],[7,8]);
                                   [ 5  6 ]
(%o2)                              [      ]
                                   [ 7  8 ]
(%i3) a.b;
                                  [ 19  22 ]
(%o3)                             [        ]
                                  [ 43  50 ]
(%i4) determinant(a);
(%o4)                                 - 2
(%i5) invert_by_lu (a);
                                 [ - 2   1  ]
                                 [          ]
(%o5)                            [  3     1 ]
                                 [  -   - - ]
                                 [  2     2 ]
(%i6) invert_by_lu (b);
                                 [ - 4   3  ]
                                 [          ]
(%o6)                            [  7     5 ]
                                 [  -   - - ]
                                 [  2     2 ]
(%i7) 
Run Example
? invert_by_lu;

 -- Function: invert_by_lu (<M>, <(rng generalring)>)
     Invert a matrix <M> by using the LU factorization.  The LU
     factorization is done using the ring <rng>.


(%o1)                                true
(%i2) 
Run Example
a:matrix([a,b],[c,d]);
                                   [ a  b ]
(%o1)                              [      ]
                                   [ c  d ]
(%i2) b:matrix([e,f],[g,h]);
                                   [ e  f ]
(%o2)                              [      ]
                                   [ g  h ]
(%i3) a.b;
                           [ b g + a e  b h + a f ]
(%o3)                      [                      ]
                           [ d g + c e  d h + c f ]
(%i4) determinant(a);
(%o4)                              a d - b c
(%i5) invert_by_lu (a) ;
                      [     b c                        ]
                      [ ----------- + 1                ]
                      [        b c                     ]
                      [ a (d - ---)                    ]
                      [         a               b      ]
                      [ ---------------  - ----------- ]
                      [        a                  b c  ]
(%o5)                 [                    a (d - ---) ]
                      [                            a   ]
                      [                                ]
                      [         c              1       ]
                      [  - -----------      -------    ]
                      [           b c           b c    ]
                      [    a (d - ---)      d - ---    ]
                      [            a             a     ]
(%i6) 

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