eigen1

631 days ago by gettrick

A = maxima('n:matrix([exp(2*pi*%i*k/q),exp(2*pi*%i*k/q)],[exp(-2*pi*%i*k/q),-exp(-2*pi*%i*k/q)])');A 
        
matrix([%e^(2*%i*k*pi/q),%e^(2*%i*k*pi/q)],[%e^-(2*%i*k*pi/q),-%e^-(2*%i\
*k*pi/q)])
matrix([%e^(2*%i*k*pi/q),%e^(2*%i*k*pi/q)],[%e^-(2*%i*k*pi/q),-%e^-(2*%i*k*pi/q)])
print(A) 
        
                      [    2 %i k pi       2 %i k pi   ]
                      [    ---------       ---------   ]
                      [        q               q       ]
                      [  %e              %e            ]
                      [                                ]
                      [     2 %i k pi        2 %i k pi ]
                      [   - ---------      - --------- ]
                      [         q                q     ]
                      [ %e             - %e            ]
                      [    2 %i k pi       2 %i k pi   ]
                      [    ---------       ---------   ]
                      [        q               q       ]
                      [  %e              %e            ]
                      [                                ]
                      [     2 %i k pi        2 %i k pi ]
                      [   - ---------      - --------- ]
                      [         q                q     ]
                      [ %e             - %e            ]
x=A.eigenvalues();print(x) 
        
        2 %i k pi         8 %i k pi       4 %i k pi          4 %i k pi
      - ---------         ---------       ---------          ---------
            q                 q               q                  q
    %e            (sqrt(%e          + 6 %e          + 1) - %e          +
1)
[[-
-----------------------------------------------------------------------,

                                       2
    2 %i k pi         8 %i k pi       4 %i k pi          4 %i k pi
  - ---------         ---------       ---------          ---------
        q                 q               q                  q
%e            (sqrt(%e          + 6 %e          + 1) + %e          - 1)
-----------------------------------------------------------------------]\
, 
                                   2
[1, 1]]
        2 %i k pi         8 %i k pi       4 %i k pi          4 %i k pi
      - ---------         ---------       ---------          ---------
            q                 q               q                  q
    %e            (sqrt(%e          + 6 %e          + 1) - %e          + 1)
[[- -----------------------------------------------------------------------, 
                                       2
    2 %i k pi         8 %i k pi       4 %i k pi          4 %i k pi
  - ---------         ---------       ---------          ---------
        q                 q               q                  q
%e            (sqrt(%e          + 6 %e          + 1) + %e          - 1)
-----------------------------------------------------------------------], 
                                   2
[1, 1]]
A = maxima('n:matrix([1,0,0,1],[0,1,1,0],[1,0,0,-1],[0,1,-1,0])');A=A/sqrt(2);print(A) 
        
                  [    1                             1     ]
                  [ -------     0         0       -------  ]
                  [ sqrt(2)                       sqrt(2)  ]
                  [                                        ]
                  [             1         1                ]
                  [    0     -------   -------       0     ]
                  [          sqrt(2)   sqrt(2)             ]
                  [                                        ]
                  [    1                              1    ]
                  [ -------     0         0      - ------- ]
                  [ sqrt(2)                        sqrt(2) ]
                  [                                        ]
                  [             1          1               ]
                  [    0     -------  - -------      0     ]
                  [          sqrt(2)    sqrt(2)            ]
                  [    1                             1     ]
                  [ -------     0         0       -------  ]
                  [ sqrt(2)                       sqrt(2)  ]
                  [                                        ]
                  [             1         1                ]
                  [    0     -------   -------       0     ]
                  [          sqrt(2)   sqrt(2)             ]
                  [                                        ]
                  [    1                              1    ]
                  [ -------     0         0      - ------- ]
                  [ sqrt(2)                        sqrt(2) ]
                  [                                        ]
                  [             1          1               ]
                  [    0     -------  - -------      0     ]
                  [          sqrt(2)    sqrt(2)            ]
x=A.eigenvalues();print(x) 
        
             sqrt(2) %i - sqrt(2)  sqrt(2) %i + sqrt(2)
    [[- 1, - --------------------, --------------------, 1], [1, 1, 1,
1]]
                      2                     2
             sqrt(2) %i - sqrt(2)  sqrt(2) %i + sqrt(2)
    [[- 1, - --------------------, --------------------, 1], [1, 1, 1, 1]]
                      2                     2
A = maxima('n:matrix([exp(2*pi*%i/3),0,0,exp(2*pi*%i/3)],[0,exp(2*pi*%i/3),exp(2*pi*%i/3),0],[exp(2*pi*%i/3),0,0,exp(2*pi*%i/3)],[0,exp(2*pi*%i/3),exp(2*pi*%i/3),0])');print(A) 
       
p=exp(2*pi*%i/3);p 
       
s=4;s