### Related

K:matrix([-2*k,k,0.0]...

eigenvalues(K);

Calculate

K:matrix([-2*k,k,0.0]...

eigenvalues(K);

Calculate

K:matrix([-2*k,k,0.0]...

eigenvalues(K);

Calculate

K:matrix([-2*k,k,0.0]...

eigenvalues(K);

Calculate

K:matrix([-2*k,k,0.0]...

eigenvalues(K);

Calculate

K:matrix([-2*k,k,0.0]...

eigenvalues(K);

Calculate

K:matrix([-2*k,k,0.0]...

eigenvalues(K);

Calculate

K:matrix([-2*k,k,0.0]...

eigenvalues(K);

Calculate

K:matrix([-2*k,k,0.0]...

eigenvalues(K);

Calculate

K:matrix([-2*k,k,0.0]...

eigenvalues(K);

Calculate

Run Example
```(%i1)load(eigen);
(%o1)           /usr/share/maxima/5.21.1/share/matrix/eigen.mac
(%i2) K:matrix([-2*k,k,0.0],[k,-2*k,k],[0,k,-2*k]);
[ - 2 k    k     0.0  ]
[                     ]
(%o2)                       [   k    - 2 k    k   ]
[                     ]
[   0      k    - 2 k ]
(%i3) eigenvalues(K);
(%o3)      [[(- sqrt(2) - 2) k, (sqrt(2) - 2) k, - 2 k], [1, 1, 1]]
(%i4) eigenvectors(K);
(%o4) [[[(- sqrt(2) - 2) k, (sqrt(2) - 2) k, - 2 k], [1, 1, 1]],
[[[1, - sqrt(2), 1]], [[1, sqrt(2), 1]], [[1, 0, - 1]]]]
(%o5)           /usr/share/maxima/5.21.1/share/vector/vect.mac
(%i6) uvect(matrix([1,-sqrt(2),1]));
[ 1       1     1 ]
(%o6)                         [ -  - -------  - ]
[ 2    sqrt(2)  2 ]
(%i7) uvect(matrix([1, sqrt(2), 1]));
[ 1     1     1 ]
(%o7)                          [ -  -------  - ]
[ 2  sqrt(2)  2 ]
(%i8) uvect([1, 0, -1]);
1             1
(%o8)                       [-------, 0, - -------]
sqrt(2)       sqrt(2)
(%i9) EK:matrix(uvect([1,-sqrt(2),1]),uvect([1, sqrt(2), 1]),uvect([1, 0,-1]));
[    1          1         1     ]
[    -     - -------      -     ]
[    2       sqrt(2)      2     ]
[                               ]
[    1         1          1     ]
(%o9)                  [    -      -------       -     ]
[    2      sqrt(2)       2     ]
[                               ]
[    1                     1    ]
[ -------      0      - ------- ]
[ sqrt(2)               sqrt(2) ]
(%i10) tEK:transpose(EK);
[     1         1         1     ]
[     -         -      -------  ]
[     2         2      sqrt(2)  ]
[                               ]
[      1        1               ]
(%o10)                 [ - -------  -------      0     ]
[   sqrt(2)  sqrt(2)            ]
[                               ]
[     1         1          1    ]
[     -         -     - ------- ]
[     2         2       sqrt(2) ]
(%i11) uvect(matrix([1,-sqrt(2),1])).K;
[      k                             k        ]
(%o11)          [ - ------- - k  sqrt(2) k + k  - ------- - k ]
[   sqrt(2)                       sqrt(2)     ]
(%i12) ```
Run Example
```K:matrix([-2*k,k,0.0],[k,-2*k,k],[0,k,-2*k]);
[ - 2 k    k     0.0  ]
[                     ]
(%o1)                       [   k    - 2 k    k   ]
[                     ]
[   0      k    - 2 k ]
(%o2)           /usr/share/maxima/5.21.1/share/matrix/eigen.mac
(%i3) eigenvalues(K);
(%o3)      [[(- sqrt(2) - 2) k, (sqrt(2) - 2) k, - 2 k], [1, 1, 1]]
(%i4) eigenvectors(K);
(%o4) [[[(- sqrt(2) - 2) k, (sqrt(2) - 2) k, - 2 k], [1, 1, 1]],
[[[1, - sqrt(2), 1]], [[1, sqrt(2), 1]], [[1, 0, - 1]]]]
(%o5)           /usr/share/maxima/5.21.1/share/vector/vect.mac
(%i6) uvect(matrix([1,-sqrt(2),1]));
[ 1       1     1 ]
(%o6)                         [ -  - -------  - ]
[ 2    sqrt(2)  2 ]
(%i7) uvect(matrix([1, sqrt(2), 1]));
[ 1     1     1 ]
(%o7)                          [ -  -------  - ]
[ 2  sqrt(2)  2 ]
(%i8) uvect([1, 0, -1]);
1             1
(%o8)                       [-------, 0, - -------]
sqrt(2)       sqrt(2)
(%i9) EK:matrix(uvect([1,-sqrt(2),1]),uvect([1, sqrt(2), 1]),uvect([1, 0,-1]));
[    1          1         1     ]
[    -     - -------      -     ]
[    2       sqrt(2)      2     ]
[                               ]
[    1         1          1     ]
(%o9)                  [    -      -------       -     ]
[    2      sqrt(2)       2     ]
[                               ]
[    1                     1    ]
[ -------      0      - ------- ]
[ sqrt(2)               sqrt(2) ]
(%i10) tEK:transpose(EK);
[     1         1         1     ]
[     -         -      -------  ]
[     2         2      sqrt(2)  ]
[                               ]
[      1        1               ]
(%o10)                 [ - -------  -------      0     ]
[   sqrt(2)  sqrt(2)            ]
[                               ]
[     1         1          1    ]
[     -         -     - ------- ]
[     2         2       sqrt(2) ]
(%i11) ```
Run Example
```load(eigen);
(%o1)           /usr/share/maxima/5.21.1/share/matrix/eigen.mac
(%i2) K:matrix([-2*k,k,0.0],[k,-2*k,k],[0,k,-2*k]);
[ - 2 k    k     0.0  ]
[                     ]
(%o2)                       [   k    - 2 k    k   ]
[                     ]
[   0      k    - 2 k ]
(%i3) eigenvalues(K);
(%o3)      [[(- sqrt(2) - 2) k, (sqrt(2) - 2) k, - 2 k], [1, 1, 1]]
(%i4) eigenvectors(K);
(%o4) [[[(- sqrt(2) - 2) k, (sqrt(2) - 2) k, - 2 k], [1, 1, 1]],
[[[1, - sqrt(2), 1]], [[1, sqrt(2), 1]], [[1, 0, - 1]]]]
(%o5)           /usr/share/maxima/5.21.1/share/vector/vect.mac
(%i6) uvect(matrix([1,-sqrt(2),1]));
[ 1       1     1 ]
(%o6)                         [ -  - -------  - ]
[ 2    sqrt(2)  2 ]
(%i7) uvect(matrix([1, sqrt(2), 1]));
[ 1     1     1 ]
(%o7)                          [ -  -------  - ]
[ 2  sqrt(2)  2 ]
(%i8) uvect([1, 0, -1]);
1             1
(%o8)                       [-------, 0, - -------]
sqrt(2)       sqrt(2)
(%i9) EK:matrix(uvect([1,-sqrt(2),1]),uvect([1, sqrt(2), 1]),uvect([1, 0,-1]));
[    1          1         1     ]
[    -     - -------      -     ]
[    2       sqrt(2)      2     ]
[                               ]
[    1         1          1     ]
(%o9)                  [    -      -------       -     ]
[    2      sqrt(2)       2     ]
[                               ]
[    1                     1    ]
[ -------      0      - ------- ]
[ sqrt(2)               sqrt(2) ]
(%i10) tEK:transpose(EK);
[     1         1         1     ]
[     -         -      -------  ]
[     2         2      sqrt(2)  ]
[                               ]
[      1        1               ]
(%o10)                 [ - -------  -------      0     ]
[   sqrt(2)  sqrt(2)            ]
[                               ]
[     1         1          1    ]
[     -         -     - ------- ]
[     2         2       sqrt(2) ]
(%i11) ```

### Related Help

Help for Eigenvalues

Help for Eigenvectors