> with(linalg):
Warning, the protected names norm and trace have been redefined and
unprotected

> delta:=matrix(4,4,[1,0,0,0, 0,1,0,0, 0,0,1,0,  0,0,0,1]);

                              [1    0    0    0]
                              [                ]
                              [0    1    0    0]
                     delta := [                ]
                              [0    0    1    0]
                              [                ]
                              [0    0    0    1]

> lA:=matrix(4,4,[0,l,0,0,  0,0,l/EI,0,  0,0,0,l,  mu*omega^2*l,0,0,0]);

                      [     0         l     0      0]
                      [                             ]
                      [                     l       ]
                      [     0         0    ----    0]
                lA := [                     EI      ]
                      [                             ]
                      [     0         0     0      l]
                      [                             ]
                      [        2                    ]
                      [mu omega  l    0     0      0]

> cp:=charpoly(lA,lambda);

                                 4              2  4
                          -lambda  EI + mu omega  l
                  cp := - --------------------------
                                      EI

> solve(cp,lambda);

           2   3 1/4             2   3 1/4
  (mu omega  EI )    l  (mu omega  EI )    l I
  --------------------, ----------------------,
           EI                     EI

                   2   3 1/4                2   3 1/4
          (mu omega  EI )    l  -I (mu omega  EI )    l
        - --------------------, -----------------------
                   EI                     EI

# Im folgenden werden die Koeffizienten psi0 bis psi3 berechnet, aber
# aus Platzgrnden nicht ausgedruckt.
> solve({psi[0]+gamma*psi[1]+gamma^2*psi[2]+gamma^3*psi[3]=exp(gamma),
> psi[0]-gamma*psi[1]+gamma^2*psi[2]-gamma^3*psi[3]=exp(-gamma),
> psi[0]+I*gamma*psi[1]-gamma^2*psi[2]-I*gamma^3*psi[3]=exp(I*gamma),
> psi[0]-I*gamma*psi[1]-gamma^2*psi[2]+I*gamma^3*psi[3]=exp(-I*gamma)},
> { psi[0], psi[1], psi[2], psi[3]}):
# 
> U:=evalm(psi[0]*delta+psi[1]*lA+psi[2]*multiply(lA,lA)+psi[3]*multiply
> (lA,lA,lA));

  U :=

        [                            2           3]
        [                    psi[2] l    psi[3] l ]
        [psi[0] , psi[1] l , --------- , ---------]
        [                       EI          EI    ]

        [        3         2                               2]
        [psi[3] l  mu omega             psi[1] l   psi[2] l ]
        [------------------- , psi[0] , -------- , ---------]
        [        EI                        EI         EI    ]

        [               2  2                  2  3
        [psi[2] mu omega  l  , psi[3] mu omega  l  , psi[0] ,

                ]
        psi[1] l]

        [
        [               2                    2  2
        [psi[1] mu omega  l , psi[2] mu omega  l  ,
        [

                3         2         ]
        psi[3] l  mu omega          ]
        ------------------- , psi[0]]
                EI                  ]

> 
> 
