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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) 
[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] [apply1,assume,defrule,diff,ev,ident,inf,integrate,load,matrix,sqrt,transpose] [assume,load,ratsimp,solve,sqrt] [atan,cos,diff,find_root,kill,matrix,phi,plot2d,plot3d,ratsimp,rhs,sin,solve,sqrt,subst] [atan,cos,diff,kill,matrix,phi,plot2d,plot3d,ratsimp,rhs,sin,solve,sqrt,subst] [atan,cos,kill,matrix,phi,plot2d,plot3d,ratsimp,rhs,sin,solve,sqrt,subst] [bfloat,ev,integrate,solve,sqrt] [charpoly,echelon,eigenvectors,invert,matrix,ratsimp,solve] [charpoly,eigenvalues,expand,invert,matrix,solve] [charpoly,eigenvectors,invert,matrix,ratsimp,solve] [charpoly,eigenvectors,matrix,ratsimp,solve] [charpoly,matrix,ratsimp,solve] [coeff,expand,factor,ratsimp,resultant,solve,sqrt,subst] [conjugate,matrix,ratsimp,sqrt,transpose] [cos,define,ev,load,matrix,numer,solve,sqrt] [cos,eliminate,ev,linsolve,matrix,ratsimp,sin,sqrt] [cos,matrix,ratsimp,rhs,sin,solve,subst,transpose,xthru] [cos,matrix,ratsimp,sin,solve,transpose] [delta,equal,is,part,ratsimp,rhs,solve,sqrt] [determinant,eigenvalues,eigenvectors,ident,load,matrix,ratsimp,solve,sqrt,transpose] [determinant,eigenvalues,invert,lambda,matrix,radcan,solve,sqrt] [determinant,let,matrix,ratsimp,scanmap,simp,solve,subst] [determinant,matrix,ratsimp,solve] [diff,display2d,facsum,false,ratsimp,solve,sqrt] [diff,ev,float,random,rhs,sin,solve,sqrt] [diff,ev,matrix,sqrt] [diff,ev,ratsimp,solve,sqrt] [diff,ev,ratsimp,solve] [eigenvalues,eigenvectors,load,matrix,ratsimp,sqrt,transpose] [eigenvalues,eigenvectors,load,matrix,sqrt,transpose] [eigenvalues,eigenvectors,load,matrix,sqrt] [eigenvalues,ev,matrix,radcan,solve,sqrt] [eigenvalues,ev,matrix,ratsimp,solve,sqrt] [eigenvalues,ev,matrix,ratsimp,solve] [eigenvalues,load,matrix,solve] [eigenvalues,matrix,sqrt] [ev,expand,ratsimp,solve] [ev,factor,ratsimp,rhs,solve] [ev,ratsimp,rhs,solve] [ev,solve,sqrt] [expand,expandwrt,ratsimp,solve,sqrt] [expand,factor,gcd,mod,ratsimp,solve,sqrt] [float,last,matrix,plot2d,ratsimp,solve,sqrt] [float,last,matrix,ratsimp,solve,sqrt] [invert,load,matrix,ratsimp,row,solve] [invert,matrix,ratsimp,solve] [last,matrix,plot2d,ratsimp,solve,sqrt] [matrix,ratsimp,sqrt] [ratsimp,solve,sqrt]

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