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detout-doallmxops-doscmxops-exp-false-invert-matrix-sqrt-true

M: matrix ([-1, -0.2,...

detout: true;

doallmxops: false;

Calculate

detout-factor-invert-matrix

A: matrix([(M+m)*s^2,...

factor(invert(A)), de...

B: matrix([1,1],[0,1/...

Calculate

detout-doallmxops-doscmxops-exp-false-invert-matrix-sqrt-true

M: matrix ([-1, -0.2,...

detout: true;

doallmxops: false;

Calculate

detout-doallmxops-doscmxops-false-invert-matrix-true

m: matrix ([a, b, c, ...

detout: true;

doallmxops: false;

Calculate

detout-false-fpprec-load-numer-ratepsilon-transpose-true

load ("vector_rebuild");

load("vect");

numer:false;

Calculate

detout-doallmxops-doscmxops-false-invert-matrix-true

M: matrix ([a, b], [c...

detout: true;

doallmxops: false;

Calculate

detout-doallmxops-doscmxops-exp-false-invert-matrix-sqrt-true

M: matrix ([1, 0.2, 0...

detout: true;

doallmxops: false;

Calculate

detout-doallmxops-doscmxops-exp-false-invert-matrix-sqrt-trigsimp-true

M: matrix ([-1, -0.2,...

detout: true;

doallmxops: false;

Calculate

detout-load-matrix

load(linearalgebra);

m : matrix([a[0][0],a...

moore_penrose_pseudoi...

Calculate

detout-doallmxops-doscmxops-exp-false-invert-matrix-sqrt-true

M: matrix ([1, 0.2, 0...

detout: true;

doallmxops: false;

Calculate

detout

Run Example
(%i1)"*"/* Beispiele von Richard H. Rand */;
(%o1)                                  *
(%i2) powerdisp:true;
(%o2)                                true
(%i3) m:matrix([0,1,a],[1,0,1],[1,1,0]);
                                  [ 0  1  a ]
                                  [         ]
(%o3)                             [ 1  0  1 ]
                                  [         ]
                                  [ 1  1  0 ]
(%i4) transpose (m);
                                  [ 0  1  1 ]
                                  [         ]
(%o4)                             [ 1  0  1 ]
                                  [         ]
                                  [ a  1  0 ]
(%i5) determinant (m);
(%o5)                                1 + a
(%i6) m1:invert (m), detout;
                               [ - 1   a    1  ]
                               [               ]
                               [  1   - a   a  ]
                               [               ]
                               [  1    1   - 1 ]
(%o6)                          -----------------
                                     1 + a
(%i7) m2:m.m1;
                                      [ - 1   a    1  ]
                                      [               ]
                                      [  1   - a   a  ]
                       [ 0  1  a ]    [               ]
                       [         ]    [  1    1   - 1 ]
(%o7)                  [ 1  0  1 ] . (-----------------)
                       [         ]          1 + a
                       [ 1  1  0 ]
(%i8) m3:expand(m2);
                [   1       a                                 ]
                [ ----- + -----        0              0       ]
                [ 1 + a   1 + a                               ]
                [                                             ]
                [                  1       a                  ]
(%o8)           [       0        ----- + -----        0       ]
                [                1 + a   1 + a                ]
                [                                             ]
                [                                 1       a   ]
                [       0              0        ----- + ----- ]
                [                               1 + a   1 + a ]
(%i9) m4:factor(m3);
                                  [ 1  0  0 ]
                                  [         ]
(%o9)                             [ 0  1  0 ]
                                  [         ]
                                  [ 0  0  1 ]
(%i10) eigenwerte:eigenvalues(m);
             - 1 + sqrt(5 + 4 a)  1 + sqrt(5 + 4 a)
(%o10)   [[- -------------------, -----------------, - 1], [1, 1, 1]]
                      2                   2
(%i11) 
Run Example
"*"/* Beispiele von Richard H. Rand */;
(%o1)                                  *
(%i2) powerdisp:true;
(%o2)                                true
(%i3) ’diff (y, x, 2) + ’diff (y, x) + y;
(%o3)                   y + diff(y, x) + diff(y, x, 2)
(%i4) ode2 (%o11, y, x);
(%t4)                                %o11

                                     msg1

(%o4)                                false
(%i5) m:matrix([0,1,a],[1,0,1],[1,1,0]);
                                  [ 0  1  a ]
                                  [         ]
(%o5)                             [ 1  0  1 ]
                                  [         ]
                                  [ 1  1  0 ]
(%i6) transpose (m);
                                  [ 0  1  1 ]
                                  [         ]
(%o6)                             [ 1  0  1 ]
                                  [         ]
                                  [ a  1  0 ]
(%i7) determinant (m);
(%o7)                                1 + a
(%i8) m1:invert (m), detout;
                               [ - 1   a    1  ]
                               [               ]
                               [  1   - a   a  ]
                               [               ]
                               [  1    1   - 1 ]
(%o8)                          -----------------
                                     1 + a
(%i9) m2:m.m1;
                                      [ - 1   a    1  ]
                                      [               ]
                                      [  1   - a   a  ]
                       [ 0  1  a ]    [               ]
                       [         ]    [  1    1   - 1 ]
(%o9)                  [ 1  0  1 ] . (-----------------)
                       [         ]          1 + a
                       [ 1  1  0 ]
(%i10) m3:expand(m2);
                [   1       a                                 ]
                [ ----- + -----        0              0       ]
                [ 1 + a   1 + a                               ]
                [                                             ]
                [                  1       a                  ]
(%o10)          [       0        ----- + -----        0       ]
                [                1 + a   1 + a                ]
                [                                             ]
                [                                 1       a   ]
                [       0              0        ----- + ----- ]
                [                               1 + a   1 + a ]
(%i11) m4:factor(m3);
                                  [ 1  0  0 ]
                                  [         ]
(%o11)                            [ 0  1  0 ]
                                  [         ]
                                  [ 0  0  1 ]
(%i12) 
Run Example
A: matrix([(M+m)*s^2,m*l*s^2],[s^2,l*s^2-g]);
                           [  2                2  ]
                           [ s  (M + m)   l m s   ]
(%o1)                      [                      ]
                           [      2         2     ]
                           [     s       l s  - g ]
(%i2) B: matrix([1,1],[0,1/m]);
                                   [ 1  1 ]
                                   [      ]
(%o2)                              [    1 ]
                                   [ 0  - ]
                                   [    m ]
(%i3) invert(A), detout;
                           [    2              2  ]
                           [ l s  - g   - l m s   ]
                           [                      ]
                           [      2     2         ]
                           [   - s     s  (M + m) ]
(%o3)                   ------------------------------
                         2     2                     4
                        s  (l s  - g) (M + m) - l m s
(%i4) C: factor(invert(A).B);
            [           2                                        ]
            [        l s  - g                       g            ]
            [ -----------------------  - ----------------------- ]
            [  2     2                    2     2                ]
(%o4)       [ s  (l s  M - g M - g m)    s  (l s  M - g M - g m) ]
            [                                                    ]
            [            1                        M              ]
            [  - ------------------     ----------------------   ]
            [       2                         2                  ]
            [    l s  M - g M - g m     m (l s  M - g M - g m)   ]
(%i5) D: factor([1,l].C);
           [                                     2                ]
           [              g                   l s  M - g m        ]
(%o5)      [ - -----------------------  ------------------------- ]
           [    2     2                    2     2                ]
           [   s  (l s  M - g M - g m)  m s  (l s  M - g M - g m) ]
(%i6) 

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