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eigenvalues-eigenvectors-load-matrix-sqrt-transpose

load(eigen);

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

eigenvalues(K);

Calculate

eigenvalues-eigenvectors-load-matrix-sqrt-transpose

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

load(eigen);

eigenvalues(K);

Calculate

eigenvalues-eigenvectors-load-matrix-sqrt-transpose

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

load(eigen);

eigenvalues(K);

Calculate

eigenvalues-eigenvectors-load-matrix-sqrt-transpose

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

load(eigen);

eigenvalues(K);

Calculate

eigenvalues-eigenvectors-load-matrix-sqrt-transpose

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

load(eigen);

eigenvalues(K);

Calculate

eigenvalues-eigenvectors-load-matrix-sqrt-transpose

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

load(eigen);

eigenvalues(K);

Calculate

eigenvalues-eigenvectors-load-matrix-sqrt-transpose

load(eigen);

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

eigenvalues(K);

Calculate

eigenvalues-eigenvectors-load-matrix-sqrt-transpose

load(eigen);

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

eigenvalues(K);

Calculate

eigenvalues-eigenvectors-load-matrix-sqrt-transpose

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

load(eigen);

eigenvalues(K);

Calculate

eigenvalues-eigenvectors-load-matrix-sqrt-transpose

load(eigen);

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

eigenvalues(K);

Calculate

[eigenvalues,eigenvectors,load,matrix,sqrt,transpose]

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]]]]
(%i5) load(vect);
(%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 ]
(%i2) load(eigen);
(%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]]]]
(%i5) load(vect);
(%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]]]]
(%i5) load(vect);
(%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) 
[addcol,addrow,diff,do,ev,genmatrix,invert,kill,load,matrix,plot2d,romberg,sqrt,submatrix] [addcol,addrow,diff,ev,genmatrix,invert,kill,length,lmax,lmin,load,matrix,plot2d,romberg,sqrt,submatrix] [append,apply,ctranspose,do,eigenvectors,false,load,matrix] [apply1,assume,defrule,diff,ev,ident,inf,integrate,load,matrix,sqrt,transpose] [args,asin,atan2,block,cos,flatten,float,ident,length,make_random_state,makelist,matrix,set_random_state,sin,sqrt,subst,transpose] [args,asin,atan2,block,cos,flatten,float,ident,length,make_random_state,makelist,matrix,set_random_state,sin,sqrt,transpose] [args,cos,load,matrix,plot2d,sin,sqrt] [asin,float,ident,mat_norm,matrix,max,sqrt,transpose] [asin,float,ident,mat_norm,matrix,sqrt,transpose] [bfloat,eigenvectors,load,matrix] [charpoly,determinant,eigenvalues,eigenvectors,ident,invert,load,matrix] [charpoly,eigenvalues,expand,gramschmidt,invert,load,matrix,sqrt,transpose] [conjugate,matrix,ratsimp,sqrt,transpose] [cos,eigenvalues,invert,matrix,numer,sin,transpose,true] [cos,load,matrix,plot2d,sin,sqrt] [determinant,diagmatrix,eigenvectors,invert,matrix,modulus,solve,transpose,triangularize] [determinant,draw,draw3d,expand,load,matrix,transpose,true] [determinant,draw,draw3d,float,load,matrix,sqrt] [determinant,eigenvalues,eigenvectors,ident,invert,matrix,rank,submatrix,transpose] [determinant,eigenvalues,eigenvectors,ident,load,matrix,ratsimp,solve,sqrt,transpose] [determinant,eigenvalues,ident,invert,matrix,rank,submatrix,transpose] [determinant,load,matrix,transpose] [diag_matrix,eigenvectors,matrix,transpose] [eigenvalues,eigenvectors,float,floor,matrix] [eigenvalues,eigenvectors,float,matrix] [eigenvalues,eigenvectors,invert,matrix] [eigenvalues,eigenvectors,lambda,matrix] [eigenvalues,eigenvectors,load,matrix,ratsimp,sqrt,transpose] [eigenvalues,eigenvectors,load,matrix,sqrt,transpose] [eigenvalues,eigenvectors,load,matrix,sqrt] [eigenvalues,eigenvectors,load,matrix] [eigenvalues,eigenvectors,matrix] [eigenvalues,ev,matrix,ratsimp,solve,sqrt] [eigenvalues,invert,matrix,transpose] [eigenvalues,load,matrix,solve] [eigenvalues,load,matrix] [eigenvalues,matrix,sqrt] [eigenvalues,matrix,transpose] [eigenvectors,ident,matrix,sqrt,transpose] [eigenvectors,load,matrix] [eigenvectors,matrix,sqrt,transpose] [eigenvectors,matrix,sqrt] [eigenvectors,matrix,transpose] [float,kill,length,load,matrix,sqrt,transpose] [float,kill,load,matrix,sqrt,transpose] [invert,matrix,sin,sqrt,transpose] [load,matrix,sqrt] [load,matrix,transpose] [matrix,nullity,rank,sqrt,transpose] [matrix,sqrt,transpose]

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