### Related

##### eigenvalues-ev-matrix-ratsimp-solve-sqrt

A:matrix([a, (sqrt(5)...

B:ev(A,a=5);

sol:ratsimp(solve(B[1...

Calculate

##### eigenvalues-ev-matrix-ratsimp-solve-sqrt

A:matrix([a, (sqrt(5)...

B:ev(A,a=0);

sol:solve(B[1,1]+B[2,...

Calculate

##### eigenvalues-ev-matrix-ratsimp-solve-sqrt

A:matrix([a, -a^2-a*d...

B:ev(A,a=0);

sol:solve(B[1,1]+B[2,...

Calculate

##### eigenvalues-ev-matrix-ratsimp-solve-sqrt

A:matrix([a,(-a^2-d^2...

dd:solve(A[1,1]+A[2,1...

ev(dd,a=2);

Calculate

##### eigenvalues-ev-matrix-ratsimp-solve-sqrt

A:matrix([a,(-a^2-d^2...

dd:solve(A[1,1]+A[2,1...

ev(dd,a=1);

Calculate

##### eigenvalues-ev-matrix-ratsimp-solve-sqrt

A:matrix([a, -a^2-a*d...

B:ev(A,a=0);

sol:solve(B[1,1]+B[2,...

Calculate

##### eigenvalues-ev-matrix-ratsimp-solve-sqrt

A:matrix([a, (sqrt(5)...

B:ev(A,a=0);

sol:solve(B[1,1]+B[2,...

Calculate

##### eigenvalues-ev-matrix-ratsimp-solve-sqrt

A:matrix([a, (sqrt(5)...

B:ev(A,a=-1);

sol:ratsimp(solve(B[1...

Calculate

##### eigenvalues-ev-matrix-ratsimp-solve-sqrt

A:matrix([a, (sqrt(5)...

B:ev(A,a=0);

sol:ratsimp(solve(B[1...

Calculate

##### eigenvalues-ev-matrix-ratsimp-solve-sqrt

A:matrix([a,(-a^2-d^2...

dd:solve(A[1,1]+A[2,1...

ev(dd,a=1);

Calculate

### [eigenvalues,ev,matrix,ratsimp,solve,sqrt]

Run Example
```(%i1)A:matrix([a, (sqrt(5)-1)*(a+d)^2/2-a^2-a*d-d^2],[1,d]);
[                         2                 ]
[    (sqrt(5) - 1) (d + a)     2          2 ]
(%o1)            [ a  ---------------------- - d  - a d - a  ]
[              2                            ]
[                                           ]
[ 1                    d                    ]
(%i2) B:ev(A,a=4);
[                         2                 ]
[    (sqrt(5) - 1) (d + 4)     2            ]
(%o2)            [ 4  ---------------------- - d  - 4 d - 16 ]
[              2                            ]
[                                           ]
[ 1                    d                    ]
(%i3) sol:ratsimp(solve(B[1,1]+B[2,1] - (B[1,2]+B[2,2])));
5/2
sqrt(2 5    - 125) + 4 sqrt(5) - 7
(%o3) [d = - ----------------------------------,
sqrt(5) - 3
5/2
sqrt(2 5    - 125) - 4 sqrt(5) + 7
d = ----------------------------------]
sqrt(5) - 3
(%i4) C:ratsimp(ev(B,d=(sqrt(-3)+1)/2));
[      5/2                                             ]
[    (3    sqrt(5) - 19 sqrt(3)) %i + 39 sqrt(5) - 109 ]
[ 4  ------------------------------------------------- ]
(%o4)      [                            4                         ]
[                                                      ]
[                     sqrt(3) %i + 1                   ]
[ 1                   --------------                   ]
[                           2                          ]
(%i5) eigenvalues(C/(a+1));
5/2              5/2
(%o5) [[- (sqrt(2) sqrt((2 3    sqrt(5) - 5 3   ) %i + 78 sqrt(5) - 195)
5/2              5/2
- sqrt(3) %i - 9)/(4 a + 4), (sqrt(2) sqrt((2 3    sqrt(5) - 5 3   ) %i
+ 78 sqrt(5) - 195) + sqrt(3) %i + 9)/(4 a + 4)], [1, 1]]
(%i6) ```
Run Example
```A:matrix([a, (sqrt(5)-1)*(a+d)^2/2-a^2-a*d-d^2],[1,d]);
[                         2                 ]
[    (sqrt(5) - 1) (d + a)     2          2 ]
(%o1)            [ a  ---------------------- - d  - a d - a  ]
[              2                            ]
[                                           ]
[ 1                    d                    ]
(%i2) B:ev(A,a=0);
[                   2      ]
[    (sqrt(5) - 1) d     2 ]
(%o2)                    [ 0  ---------------- - d  ]
[           2              ]
[                          ]
[ 1            d           ]
(%i3) sol:ratsimp(solve(B[1,1]+B[2,1] - (B[1,2]+B[2,2])));
sqrt(2 sqrt(5) - 5) + 1      sqrt(2 sqrt(5) - 5) - 1
(%o3)    [d = - -----------------------, d = -----------------------]
sqrt(5) - 3                  sqrt(5) - 3
(%i4) C:ratsimp(ev(B,d=(sqrt(-3)+1)/2));
[                        3/2                   ]
[    (sqrt(3) sqrt(5) - 3   ) %i - sqrt(5) + 3 ]
[ 0  ----------------------------------------- ]
(%o4)          [                        4                     ]
[                                              ]
[                 sqrt(3) %i + 1               ]
[ 1               --------------               ]
[                       2                      ]
(%i5) eigenvalues(C/(a+1));
(%o5) [[- (sqrt(2) sqrt((2 sqrt(3) sqrt(5) - 5 sqrt(3)) %i - 2 sqrt(5) + 5)
- sqrt(3) %i - 1)/(4 a + 4), (sqrt(2) sqrt((2 sqrt(3) sqrt(5) - 5 sqrt(3)) %i
- 2 sqrt(5) + 5) + sqrt(3) %i + 1)/(4 a + 4)], [1, 1]]
(%i6) ```
Run Example
```A:matrix([a, (sqrt(5)-1)*(a+d)^2/2-a^2-a*d-d^2],[1,d]);
[                         2                 ]
[    (sqrt(5) - 1) (d + a)     2          2 ]
(%o1)            [ a  ---------------------- - d  - a d - a  ]
[              2                            ]
[                                           ]
[ 1                    d                    ]
(%i2) B:ev(A,a=4);
[                         2                 ]
[    (sqrt(5) - 1) (d + 4)     2            ]
(%o2)            [ 4  ---------------------- - d  - 4 d - 16 ]
[              2                            ]
[                                           ]
[ 1                    d                    ]
(%i3) sol:solve(B[1,1]+B[2,1] - (B[1,2]+B[2,2]));
5/2
sqrt(2 5    - 125) + 4 sqrt(5) - 7
(%o3) [d = - ----------------------------------,
sqrt(5) - 3
5/2
sqrt(2 5    - 125) - 4 sqrt(5) + 7
d = ----------------------------------]
sqrt(5) - 3
(%i4) C:ratsimp(ev(B,d=(sqrt(-3)+1)/2));
[      5/2                                             ]
[    (3    sqrt(5) - 19 sqrt(3)) %i + 39 sqrt(5) - 109 ]
[ 4  ------------------------------------------------- ]
(%o4)      [                            4                         ]
[                                                      ]
[                     sqrt(3) %i + 1                   ]
[ 1                   --------------                   ]
[                           2                          ]
(%i5) eigenvalues(C/(a+1));
5/2              5/2
(%o5) [[- (sqrt(2) sqrt((2 3    sqrt(5) - 5 3   ) %i + 78 sqrt(5) - 195)
5/2              5/2
- sqrt(3) %i - 9)/(4 a + 4), (sqrt(2) sqrt((2 3    sqrt(5) - 5 3   ) %i
+ 78 sqrt(5) - 195) + sqrt(3) %i + 9)/(4 a + 4)], [1, 1]]
(%i6) ```

### Related Help

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