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diagmatrix-ident-matrix

m:matrix([.99,1,0],[....

p:diagmatrix(3,x);

p*(m-ident(3))+ident(3);

Calculate

diagmatrix-matrix

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

i: diagmatrix (4, 1);

j: matrix ( [1,1,1,1]...

Calculate

diagmatrix

? diagmatrix;

Calculate

diagmatrix-matrix

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

i: diagmatrix (4, 1);

Calculate

diagmatrix

diagmatrix(3,2);

diagmatrix(3,1);

diagmatrix(4,3);

Calculate

diagmatrix-expand-jacobian-matrix-phi-ratsimp-sin

A:matrix([0,-1/L1,0],...

B:matrix([1/L1, 0], [...

x:matrix([i_inv],[u_c...

Calculate

diagmatrix

a: diagmatrix(10,0);

a[1,1]: 1;

a[2,2]: 1;

Calculate

diagmatrix

? diagmatrix;

Calculate

diagmatrix

a: diagmatrix(10,0);

a[1,1]: 1;

a[2,2]: 1;

Calculate

diagmatrix

P:diagmatrix(16,0);

P[1,5]:P[5,1]:1;

P;

Calculate

diagmatrix

Run Example
(%i1)A:matrix([0,-1/L1,0],     [1/C,0,-1/C],     [0,1/L,-Rg/L]);
                               [      1        ]
                               [ 0  - --   0   ]
                               [      L1       ]
                               [               ]
                               [ 1          1  ]
(%o1)                          [ -   0    - -  ]
                               [ C          C  ]
                               [               ]
                               [     1      Rg ]
                               [ 0   -    - -- ]
                               [     L      L  ]
(%i2) B:matrix([1/L1, 0], [0,0], [0,-1/L]);
                                  [ 1       ]
                                  [ --   0  ]
                                  [ L1      ]
                                  [         ]
(%o2)                             [ 0    0  ]
                                  [         ]
                                  [       1 ]
                                  [ 0   - - ]
                                  [       L ]
(%i3) x:matrix([i_inv],[u_c],[i_g]);
                                   [ i_inv ]
                                   [       ]
(%o3)                              [  u_c  ]
                                   [       ]
                                   [  i_g  ]
(%i4) u:matrix([u_inv],[u1*sin(theta+phi)]);
                            [        u_inv        ]
(%o4)                       [                     ]
                            [ sin(theta + phi) u1 ]
(%i5) Ad: diagmatrix(3,1) + A*T + (A*T).(A*T)/2;
           [        2                                 2            ]
           [       T             T                   T             ]
           [ 1 - ------        - --                ------          ]
           [     2 C L1          L1                2 C L1          ]
           [                                                       ]
           [                 2     2                               ]
           [                T     T                                ]
           [             - ---- - ---                 2            ]
           [     T         C L1   C L             Rg T    T        ]
(%o5)      [     -       ------------ + 1         ----- - -        ]
           [     C            2                   2 C L   C        ]
           [                                                       ]
           [                                 2  2    2             ]
           [                               Rg  T    T              ]
           [                               ------ - ---            ]
           [     2                  2         2     C L            ]
           [    T           T   Rg T         L            Rg T     ]
           [   -----        - - -----      ------------ - ---- + 1 ]
           [   2 C L        L      2            2          L       ]
           [                    2 L                                ]
(%i6) Bd: (diagmatrix(3,1) + A*T^2/2).B;
                            [   1                 ]
                            [   --         0      ]
                            [   L1                ]
                            [                     ]
                            [    2         2      ]
                            [   T         T       ]
                            [ ------     -----    ]
(%o6)                       [ 2 C L1     2 C L    ]
                            [                     ]
                            [                   2 ]
                            [               Rg T  ]
                            [           1 - ----- ]
                            [                2 L  ]
                            [   0     - --------- ]
                            [               L     ]
(%i7) h: Ad.x + Bd.u;
                            2           2
                           T       i_g T    u_c T   u_inv
(%o7) matrix([i_inv (1 - ------) + ------ - ----- + -----], 
                         2 C L1    2 C L1    L1      L1
          2     2
         T     T
      - ---- - ---                 2               2                        2
        C L1   C L             Rg T    T    u_inv T    sin(theta + phi) u1 T
[u_c (------------ + 1) + i_g (----- - -) + -------- + ----------------------
           2                   2 C L   C     2 C L1            2 C L
                     2  2    2
                   Rg  T    T                                              2
                   ------ - ---                                        Rg T
                      2     C L               sin(theta + phi) u1 (1 - -----)
   i_inv T           L            Rg T                                  2 L
 + -------], [i_g (------------ - ---- + 1) - -------------------------------
      C                 2          L                         L
                2           2
        T   Rg T     i_inv T
 + u_c (- - -----) + --------])
        L      2      2 C L
            2 L
(%i8) k(i_inv,u_c,i_g,Rg,L,phi):= h;
(%o8)                 k(i_inv, u_c, i_g, Rg, L, phi) := h
(%i9) k;
(%o9)                                  k
(%i10) j: jacobian([h],[i_inv,u_c,i_g,Rg,L,phi]);
                               [         T        ]
               [        2   ]  [       - --       ]
               [       T    ]  [         L1       ]
               [ 1 - ------ ]  [                  ]
               [     2 C L1 ]  [     2     2      ]
               [            ]  [    T     T       ]
               [     T      ]  [ - ---- - ---     ]
(%o10) matrix([[     -      ], [   C L1   C L     ], 
               [     C      ]  [ ------------ + 1 ]
               [            ]  [      2           ]
               [     2      ]  [                  ]
               [    T       ]  [            2     ]
               [   -----    ]  [    T   Rg T      ]
               [   2 C L    ]  [    - - -----     ]
                               [    L      2      ]
                               [        2 L       ]
[            2            ]
[           T             ]
[         ------          ]
[         2 C L1          ]
[                         ]
[            2            ]
[        Rg T    T        ]
[        ----- - -        ]
[        2 C L   C        ], 
[                         ]
[   2  2    2             ]
[ Rg  T    T              ]
[ ------ - ---            ]
[    2     C L            ]
[   L            Rg T     ]
[ ------------ - ---- + 1 ]
[      2          L       ]
[                         0                         ]
[                                                   ]
[                           2                       ]
[                      i_g T                        ]
[                      ------                       ]
[                      2 C L                        ], 
[                                                   ]
[          2             2                        2 ]
[      Rg T    T    u_c T    sin(theta + phi) u1 T  ]
[ i_g (----- - -) - ------ + ---------------------- ]
[        2     L        2                2          ]
[       L            2 L              2 L           ]
                  2                        2           2
             u_c T    sin(theta + phi) u1 T    i_g Rg T
matrix([0], [------ - ---------------------- - ---------], 
                  2                2                 2
             2 C L            2 C L             2 C L
        2        2  2
       T     2 Rg  T                                         2
      ---- - --------                                    Rg T
         2       3              sin(theta + phi) u1 (1 - -----)
      C L       L       Rg T                              2 L
[i_g (--------------- + ----) + -------------------------------
             2            2                    2
                         L                    L
            2                2                           2
        Rg T    T     i_inv T    Rg sin(theta + phi) u1 T
 + u_c (----- - --) - -------- - -------------------------]), 
          3      2          2                 3
         L      L      2 C L               2 L
[                 0                 ]
[                                   ]
[                           2       ]
[      cos(theta + phi) u1 T        ]
[      ----------------------       ]
[              2 C L                ]
[                                   ]])
[                                2  ]
[                            Rg T   ]
[   cos(theta + phi) u1 (1 - -----) ]
[                             2 L   ]
[ - ------------------------------- ]
[                  L                ]
(%i11) diff(h,i_inv);
                                [        2   ]
                                [       T    ]
                                [ 1 - ------ ]
                                [     2 C L1 ]
                                [            ]
                                [     T      ]
(%o11)                          [     -      ]
                                [     C      ]
                                [            ]
                                [     2      ]
                                [    T       ]
                                [   -----    ]
                                [   2 C L    ]
(%i12) D: diagmatrix(3,vals[1]);
                            [ vals     0      0   ]
                            [     1               ]
                            [                     ]
(%o12)                      [   0    vals     0   ]
                            [            1        ]
                            [                     ]
                            [   0      0    vals  ]
                            [                   1 ]
(%i13) vecs*exp(D)*vecs^-1;
                         [   vals                    ]
                         [       1                   ]
                         [ %e          1        1    ]
                         [                           ]
                         [            vals           ]
(%o13)                   [                1          ]
                         [    1     %e          1    ]
                         [                           ]
                         [                     vals  ]
                         [                         1 ]
                         [    1        1     %e      ]
(%i14) 
Run Example
A: diagmatrix(10,2);
                       [ 2  0  0  0  0  0  0  0  0  0 ]
                       [                              ]
                       [ 0  2  0  0  0  0  0  0  0  0 ]
                       [                              ]
                       [ 0  0  2  0  0  0  0  0  0  0 ]
                       [                              ]
                       [ 0  0  0  2  0  0  0  0  0  0 ]
                       [                              ]
                       [ 0  0  0  0  2  0  0  0  0  0 ]
(%o1)                  [                              ]
                       [ 0  0  0  0  0  2  0  0  0  0 ]
                       [                              ]
                       [ 0  0  0  0  0  0  2  0  0  0 ]
                       [                              ]
                       [ 0  0  0  0  0  0  0  2  0  0 ]
                       [                              ]
                       [ 0  0  0  0  0  0  0  0  2  0 ]
                       [                              ]
                       [ 0  0  0  0  0  0  0  0  0  2 ]
(%i2) 
Run Example
P:diagmatrix(16,0);
              [ 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 ]
              [                                                ]
              [ 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 ]
              [                                                ]
              [ 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 ]
              [                                                ]
              [ 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 ]
              [                                                ]
              [ 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 ]
              [                                                ]
              [ 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 ]
              [                                                ]
              [ 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 ]
              [                                                ]
              [ 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 ]
(%o1)         [                                                ]
              [ 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 ]
              [                                                ]
              [ 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 ]
              [                                                ]
              [ 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 ]
              [                                                ]
              [ 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 ]
              [                                                ]
              [ 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 ]
              [                                                ]
              [ 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 ]
              [                                                ]
              [ 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 ]
              [                                                ]
              [ 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 ]
(%i2) P[1,5]:P[5,1]:1;
(%o2)                                  1
(%i3) P;
              [ 0  0  0  0  1  0  0  0  0  0  0  0  0  0  0  0 ]
              [                                                ]
              [ 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 ]
              [                                                ]
              [ 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 ]
              [                                                ]
              [ 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 ]
              [                                                ]
              [ 1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 ]
              [                                                ]
              [ 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 ]
              [                                                ]
              [ 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 ]
              [                                                ]
              [ 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 ]
(%o3)         [                                                ]
              [ 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 ]
              [                                                ]
              [ 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 ]
              [                                                ]
              [ 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 ]
              [                                                ]
              [ 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 ]
              [                                                ]
              [ 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 ]
              [                                                ]
              [ 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 ]
              [                                                ]
              [ 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 ]
              [                                                ]
              [ 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 ]
(%i4) 

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