> with(LinearAlgebra):
> ### Pra3eis me pinakes kai dianusmata
> A:=<<1,2>|<0,1>>;
                               [1  0]
                          A := [    ]
                               [2  1]
> B:=<<0,1>|<1,1>>;
                               [0  1]
                          B := [    ]
                               [1  1]
> A.B;
                             [0  1]
                             [    ]
                             [1  3]
> v:=<x,y>;
                                 [x]
                            v := [ ]
                                 [y]
> A.v;
                           [   x   ]
                           [       ]
                           [2 x + y]
> 2*v;
                             [2 x]
                             [   ]
                             [2 y]
> ### Xwros sthlwn kai mhdenoxwros pinaka
> A:=<<1,0,1>|<0,1,1>|<2,1,0>>;
                              [1  0  2]
                              [       ]
                         A := [0  1  1]
                              [       ]
                              [1  1  0]
> Column(A,1);
                              [1]
                              [ ]
                              [0]
                              [ ]
                              [1]
> for i from 1 to 3 do
> c[i]:=Column(A,i):
> end do:
> Basis([seq(c[i],i=1..3)]);
                        [[1]  [0]  [2]]
                        [[ ]  [ ]  [ ]]
                        [[0], [1], [1]]
                        [[ ]  [ ]  [ ]]
                        [[1]  [1]  [0]]
> NullSpace(A);
                               {}
> B:=<<1,1,0>|<0,1,2>|<2,1,1>|<0,1,1>>;
                            [1  0  2  0]
                            [          ]
                       B := [1  1  1  1]
                            [          ]
                            [0  2  1  1]
> for i from 1 to 3 do
> c[i]:=Column(B,i):
> end do:
> Basis([seq(c[i],i=1..3)]);
                        [[1]  [0]  [2]]
                        [[ ]  [ ]  [ ]]
                        [[1], [1], [1]]
                        [[ ]  [ ]  [ ]]
                        [[0]  [2]  [1]]
> NullSpace(B);
                             /[-2]\ 
                             |[--]| 
                             |[3 ]| 
                             |[  ]| 
                             |[-2]| 
                             |[--]| 
                            < [3 ] >
                             |[  ]| 
                             |[ 1]| 
                             |[ -]| 
                             |[ 3]| 
                             |[  ]| 
                             \[ 1]/ 
> ### Idiotimes, xarakthristiko poluwnumo
> P:=CharacteristicPolynomial(A,t);
                          3      2          
                    P := t  - 2 t  - 2 t + 3
> idiotimes:=solve(P=0,t);
                          1   1   (1/2)  1   1   (1/2)
          idiotimes := 1, - + - 13     , - - - 13     
                          2   2          2   2        
> Id:=IdentityMatrix(3);
                              [1  0  0]
                              [       ]
                        Id := [0  1  0]
                              [       ]
                              [0  0  1]
> Q:=Determinant(A-t*Id);
                            2        3      
                    Q := 2 t  - 3 - t  + 2 t
> NullSpace(A-idiotimes[1]*Id);
                             /[-1]\ 
                             |[  ]| 
                            < [ 1] >
                             |[  ]| 
                             \[ 0]/ 
> NullSpace(A-idiotimes[2]*Id);
                        /[     4      ]\ 
                        |[------------]| 
                        |[       (1/2)]| 
                        |[-1 + 13     ]| 
                        |[            ]| 
                       < [     2      ] >
                        |[------------]| 
                        |[       (1/2)]| 
                        |[-1 + 13     ]| 
                        |[            ]| 
                        \[     1      ]/ 
> NullSpace(A-idiotimes[3]*Id);
                       /[       4     ]\ 
                       |[- -----------]| 
                       |[        (1/2)]| 
                       |[  1 + 13     ]| 
                       |[             ]| 
                      < [       2     ] >
                       |[- -----------]| 
                       |[        (1/2)]| 
                       |[  1 + 13     ]| 
                       |[             ]| 
                       \[      1      ]/