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identfor-invert-matrix

A: matrix([-Ra/La,-k/...

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

sol1: invert(s*identf...

Calculate

identfor-invert-matrix

A: matrix([-Ra/La,-k/...

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

invert(s*identfor(A)-A);

Calculate

identfor-mat_trace-matrix-sum-trace

strain(u) := matrix([...

stress(e) := b*mat_tr...

sum(sum(strain[i][j] ...

Calculate

identfor-invert-matrix

R:matrix([a11, a12, a...

I:identfor(R);

invert(I-R);

Calculate

identfor-matrix

A: matrix([-Ra/La,-k/...

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

s*identfor(A)-A;

Calculate

identfor-invert-matrix

R:matrix([a11, a12, a...

I:identfor(R);

invert(I-R);

Calculate

identfor-invert-matrix

R:matrix([a11, a12, a...

I:identfor(R);

invert(I-R);

Calculate

identfor-invert-matrix

A: matrix([-Ra/La,-k/...

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

sol1: simplify(invert...

Calculate

identfor-invert-matrix

A: matrix([-Ra/La,-k/...

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

invert(s*identfor(A)-A);

Calculate

identfor-mat_trace-matrix-trace

strain(u) := matrix([...

stress(e) := b*mat_tr...

Calculate

identfor

Run Example
(%i1)A: matrix([-Ra/La,-k/La],[k/O,0]);
                                [   Ra    k  ]
                                [ - --  - -- ]
                                [   La    La ]
(%o1)                           [            ]
                                [  k         ]
                                [  -     0   ]
                                [  O         ]
(%i2) B: matrix([1/La,0],[0,1/O]);
                                   [ 1     ]
                                   [ --  0 ]
                                   [ La    ]
(%o2)                              [       ]
                                   [     1 ]
                                   [ 0   - ]
                                   [     O ]
(%i3) invert(s*identfor(A)-A);
              [           s                        k            ]
              [   -----------------    - ---------------------- ]
              [     2                          2                ]
              [    k            Ra            k            Ra   ]
              [   ---- + s (s + --)      La (---- + s (s + --)) ]
              [   La O          La           La O          La   ]
              [                                                 ]
(%o3)         [                                    Ra           ]
              [                                s + --           ]
              [           k                        La           ]
              [ ---------------------     -----------------     ]
              [    2                        2                   ]
              [   k            Ra          k            Ra      ]
              [ (---- + s (s + --)) O     ---- + s (s + --)     ]
              [  La O          La         La O          La      ]
(%i4) 
Run Example
A1:matrix([0,1,0,0,0,0],[0,0,a23,-a23-a24,0,0],[0,0,0,0,a35,0],[0,0,0,0,-a45,0],[0,0,0,0,0,1],[0,0,0,0,0,0]);
                     [ 0  1   0        0         0    0 ]
                     [                                  ]
                     [ 0  0  a23  - a24 - a23    0    0 ]
                     [                                  ]
                     [ 0  0   0        0        a35   0 ]
(%o1)                [                                  ]
                     [ 0  0   0        0       - a45  0 ]
                     [                                  ]
                     [ 0  0   0        0         0    1 ]
                     [                                  ]
                     [ 0  0   0        0         0    0 ]
(%i2) I:s*identfor(A1);
                             [ s  0  0  0  0  0 ]
                             [                  ]
                             [ 0  s  0  0  0  0 ]
                             [                  ]
                             [ 0  0  s  0  0  0 ]
(%o2)                        [                  ]
                             [ 0  0  0  s  0  0 ]
                             [                  ]
                             [ 0  0  0  0  s  0 ]
                             [                  ]
                             [ 0  0  0  0  0  s ]
(%i3) 
Run Example
A1:matrix([0,1,0,0,0,0],[0,0,a23,-a23-a24,0,0],[0,0,0,0,a35,0],[0,0,0,0,-a45,0],[0,0,0,0,0,1],[0,0,0,0,0,0]);
                     [ 0  1   0        0         0    0 ]
                     [                                  ]
                     [ 0  0  a23  - a24 - a23    0    0 ]
                     [                                  ]
                     [ 0  0   0        0        a35   0 ]
(%o1)                [                                  ]
                     [ 0  0   0        0       - a45  0 ]
                     [                                  ]
                     [ 0  0   0        0         0    1 ]
                     [                                  ]
                     [ 0  0   0        0         0    0 ]
(%i2) I:identfor(A1);
                             [ 1  0  0  0  0  0 ]
                             [                  ]
                             [ 0  1  0  0  0  0 ]
                             [                  ]
                             [ 0  0  1  0  0  0 ]
(%o2)                        [                  ]
                             [ 0  0  0  1  0  0 ]
                             [                  ]
                             [ 0  0  0  0  1  0 ]
                             [                  ]
                             [ 0  0  0  0  0  1 ]
(%i3) C:matrix([1,0,0,0,0,0]);
(%o3)                        [ 1  0  0  0  0  0 ]
(%i4) Lambda:transpose(matrix([Lambda1,Lambda2,Lambda3,Lambda4,Lambda5,Lambda6]));
                                  [ Lambda1 ]
                                  [         ]
                                  [ Lambda2 ]
                                  [         ]
                                  [ Lambda3 ]
(%o4)                             [         ]
                                  [ Lambda4 ]
                                  [         ]
                                  [ Lambda5 ]
                                  [         ]
                                  [ Lambda6 ]
(%i5) prod:Lambda.C;
                          [ Lambda1  0  0  0  0  0 ]
                          [                        ]
                          [ Lambda2  0  0  0  0  0 ]
                          [                        ]
                          [ Lambda3  0  0  0  0  0 ]
(%o5)                     [                        ]
                          [ Lambda4  0  0  0  0  0 ]
                          [                        ]
                          [ Lambda5  0  0  0  0  0 ]
                          [                        ]
                          [ Lambda6  0  0  0  0  0 ]
(%i6) polycar:determinant(s*I-(A1-Lambda.C));
               4                 3
(%o6) Lambda2 s  + a23 (Lambda3 s  + a35 s (Lambda5 s + Lambda6))
                              2                                 5
    - (a24 + a23) s (Lambda4 s  - a45 (Lambda5 s + Lambda6)) + s  (s + Lambda1)
(%i7) 

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