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diag_matrix-matrix

m:matrix([1,2,3,4]);

diag_matrix(m);

Calculate

diag_matrix-eigenvectors-matrix-transpose

A:matrix([-1,0,0,1],[...

eigenvectors(A);

diag_matrix(A);

Calculate

diag_matrix-matrix

A: matrix([3,-1,2],[3...

B: A-diag_matrix(x,x,x);

Calculate

diag_matrix-eigenvectors-matrix-transpose

A:matrix([5,0,-4],[0,...

eigenvectors(A);

diag_matrix(A);

Calculate

diag_matrix-genmatrix-invert-lambda-transpose

A: genmatrix(lambda([...

B: matrix([1,0], [2,7...

P: diag_matrix(1/2,1/2);

Calculate

diag_matrix-matrix

m:columnvector([1,2,3...

diag_matrix(m);

Calculate

diag_matrix-gcd-load-matrix-ratfac-riemann-scurvature

load(ctensor);

(cframe_flag:false,gc...

lg:diag_matrix(-t,t^2...

Calculate

diag_matrix-matrix-transpose

a:matrix([-1,2,0,-1],...

a.transpose(a);

a.diag_matrix(2,4,2,1...

Calculate

diag_matrix

Run Example
(%i1)load(ctensor);
(%o1)          /usr/share/maxima/5.21.1/share/tensor/ctensor.mac
(%i2) (cframe_flag:false,gcd:spmod,ctrgsimp:true,ratfac:true);
(%o2)                                true
(%i3) lg:diag_matrix(-1,r*k^2,r^2,(sin(%theta)*r)^2);
                      [ - 1   0    0          0        ]
                      [                                ]
                      [       2                        ]
                      [  0   k  r  0          0        ]
(%o3)                 [                                ]
                      [             2                  ]
                      [  0    0    r          0        ]
                      [                                ]
                      [                   2          2 ]
                      [  0    0    0   sin (%theta) r  ]
(%i4) ct_coords:[t,r,%theta,%phi];
(%o4)                        [t, r, %theta, %phi]
(%i5) depends(%nu,[r,t],%lambda,[r,t]);
(%o5)                     [%nu(r, t), %lambda(r, t)]
(%i6) cmetric(false);
(%o6)                                done
(%i7) christof(mcs);
                                             1
(%t7)                          mcs        = ---
                                  2, 2, 2   2 r

                                             1
(%t8)                           mcs        = -
                                   2, 3, 3   r

                                             1
(%t9)                           mcs        = -
                                   2, 4, 4   r

                                              1
(%t10)                         mcs        = - --
                                  3, 3, 2      2
                                              k

                                        cos(%theta)
(%t11)                     mcs        = -----------
                              3, 4, 4   sin(%theta)

                                            2
                                         sin (%theta)
(%t12)                    mcs        = - ------------
                             4, 4, 2           2
                                              k

(%t13)              mcs        = - cos(%theta) sin(%theta)
                       4, 4, 3

(%o13)                               done
(%i14)  riemann(true);
                                                1
(%t14)                      riem           = - ----
                                2, 3, 2, 3        2
                                               2 r

                                                1
(%t15)                      riem           = - ----
                                2, 4, 2, 4        2
                                               2 r

                                               1
(%t16)                      riem           = ------
                                3, 3, 2, 2      2
                                             2 k  r

                                             1
(%t17)                     riem           = ---- - 1
                               3, 4, 3, 4    2
                                            k  r

                                             2
                                          sin (%theta)
(%t18)                   riem           = ------------
                             4, 4, 2, 2         2
                                             2 k  r

                                       2           2
                                    sin (%theta) (k  r - 1)
(%t19)             riem           = -----------------------
                       4, 4, 3, 3             2
                                             k  r

(%o19)                               done
(%i20) ricci(true);
                                           1
(%t20)                           ric     = --
                                    2, 2    2
                                           r

                                          2
                                       2 k  r - 1
(%t21)                       ric     = ----------
                                3, 3        2
                                         2 k  r

                                   2             2
                                sin (%theta) (2 k  r - 1)
(%t22)                ric     = -------------------------
                         4, 4               2
                                         2 k  r

(%o22)                               done
(%i23) R:scurvature();
                                      2
(%o23)                                --
                                       2
                                      r
(%i24) 
Run Example
A:matrix([0,1,1,1],[1,-2,-1,-2],[1,-1,0,-1],[1,-2,-1,-2]);
                             [ 0   1    1    1  ]
                             [                  ]
                             [ 1  - 2  - 1  - 2 ]
(%o1)                        [                  ]
                             [ 1  - 1   0   - 1 ]
                             [                  ]
                             [ 1  - 2  - 1  - 2 ]
(%i2) eigenvectors(A);
(%o2) [[[- 5, 1, 0], [1, 1, 2]], [[[1, - 2, - 1, - 2]], [[1, 0, 1, 0]], 
                                             [[1, 0, - 1, 1], [0, 1, 0, - 1]]]]
(%i3) diag_matrix(A);
                           [ [ 0   1    1    1  ] ]
                           [ [                  ] ]
                           [ [ 1  - 2  - 1  - 2 ] ]
(%o3)                      [ [                  ] ]
                           [ [ 1  - 1   0   - 1 ] ]
                           [ [                  ] ]
                           [ [ 1  - 2  - 1  - 2 ] ]
(%i4) transpose(A);
                             [ 0   1    1    1  ]
                             [                  ]
                             [ 1  - 2  - 1  - 2 ]
(%o4)                        [                  ]
                             [ 1  - 1   0   - 1 ]
                             [                  ]
                             [ 1  - 2  - 1  - 2 ]
(%i5) I:matrix([1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]);
                                [ 1  0  0  0 ]
                                [            ]
                                [ 0  1  0  0 ]
(%o5)                           [            ]
                                [ 0  0  1  0 ]
                                [            ]
                                [ 0  0  0  1 ]
(%i6) b=(-5*I-A);
                              [ - 5  - 1  - 1  - 1 ]
                              [                    ]
                              [ - 1  - 3   1    2  ]
(%o6)                     b = [                    ]
                              [ - 1   1   - 5   1  ]
                              [                    ]
                              [ - 1   2    1   - 3 ]
(%i7) 
Run Example
load(ctensor);
(%o1)          /usr/share/maxima/5.21.1/share/tensor/ctensor.mac
(%i2) (cframe_flag:false,gcd:spmod,ctrgsimp:true,ratfac:true);
(%o2)                                true
(%i3) lg:diag_matrix(-1,1,1,f(t,x));
                            [ - 1  0  0     0    ]
                            [                    ]
                            [  0   1  0     0    ]
(%o3)                       [                    ]
                            [  0   0  1     0    ]
                            [                    ]
                            [  0   0  0  f(t, x) ]
(%i4) ct_coords:[t,x,y,z];
(%o4)                            [t, x, y, z]
(%i5) cmetric(false);
(%o5)                                done
(%i6) christof(mcs);
                                        d
                                        -- (f(t, x))
                                        dt
(%t6)                      mcs        = ------------
                              1, 4, 4    2 f(t, x)

                                        d
                                        -- (f(t, x))
                                        dx
(%t7)                      mcs        = ------------
                              2, 4, 4    2 f(t, x)

                                        d
                                        -- (f(t, x))
                                        dt
(%t8)                      mcs        = ------------
                              4, 4, 1        2

                                         d
                                         -- (f(t, x))
                                         dx
(%t9)                     mcs        = - ------------
                             4, 4, 2          2

(%o9)                                done
(%i10)  riemann(true);
                                 2
                                d
                                --- (f(t, x))    d            2
                                  2             (-- (f(t, x)))
                                dt               dt
(%t10)         riem           = ------------- - ---------------
                   1, 4, 1, 4     2 f(t, x)          2
                                                  4 f (t, x)

                          2
                         d                 d              d
                        ----- (f(t, x))   (-- (f(t, x))) (-- (f(t, x)))
                        dt dx              dt             dx
(%t11) riem           = --------------- - -----------------------------
           1, 4, 2, 4      2 f(t, x)                  2
                                                   4 f (t, x)

                          2
                         d                 d              d
                        ----- (f(t, x))   (-- (f(t, x))) (-- (f(t, x)))
                        dt dx              dt             dx
(%t12) riem           = --------------- - -----------------------------
           2, 4, 1, 4      2 f(t, x)                  2
                                                   4 f (t, x)

                                 2
                                d
                                --- (f(t, x))    d            2
                                  2             (-- (f(t, x)))
                                dx               dx
(%t13)         riem           = ------------- - ---------------
                   2, 4, 2, 4     2 f(t, x)          2
                                                  4 f (t, x)

                                      2
                                     d                 d            2
                          2 f(t, x) (--- (f(t, x))) - (-- (f(t, x)))
                                       2               dt
                                     dt
(%t14)   riem           = -------------------------------------------
             4, 4, 1, 1                    4 f(t, x)

(%t15) riem           = 
           4, 4, 1, 2
                                                                 2
                     d              d                           d
                    (-- (f(t, x))) (-- (f(t, x))) - 2 f(t, x) (----- (f(t, x)))
                     dt             dx                         dt dx
                    -----------------------------------------------------------
                                             4 f(t, x)

(%t16) riem           = 
           4, 4, 2, 1
                                                                 2
                     d              d                           d
                    (-- (f(t, x))) (-- (f(t, x))) - 2 f(t, x) (----- (f(t, x)))
                     dt             dx                         dt dx
                  - -----------------------------------------------------------
                                             4 f(t, x)

                                       2
                                      d                 d            2
                           2 f(t, x) (--- (f(t, x))) - (-- (f(t, x)))
                                        2               dx
                                      dx
(%t17)  riem           = - -------------------------------------------
            4, 4, 2, 2                      4 f(t, x)

(%o17)                               done
(%i18) ricci(true);
                                    2
                                   d                 d            2
                        2 f(t, x) (--- (f(t, x))) - (-- (f(t, x)))
                                     2               dt
                                   dt
(%t18)      ric     = - -------------------------------------------
               1, 1                        2
                                        4 f (t, x)

                                                              2
                  d              d                           d
                 (-- (f(t, x))) (-- (f(t, x))) - 2 f(t, x) (----- (f(t, x)))
                  dt             dx                         dt dx
(%t19) ric     = -----------------------------------------------------------
          1, 2                              2
                                         4 f (t, x)

                                    2
                                   d                 d            2
                        2 f(t, x) (--- (f(t, x))) - (-- (f(t, x)))
                                     2               dx
                                   dx
(%t20)      ric     = - -------------------------------------------
               2, 2                        2
                                        4 f (t, x)

                                2
                               d                 d            2
(%t21) ric     = - (2 f(t, x) (--- (f(t, x))) - (-- (f(t, x)))
          4, 4                   2               dx
                               dx
                                   2
                                  d                 d            2
                     - 2 f(t, x) (--- (f(t, x))) + (-- (f(t, x))) )/(4 f(t, x))
                                    2               dt
                                  dt

(%o21)                               done
(%i22) 
[christof,depends,determinant,diag_matrix,diff,exp,gcd,invert,load,matrix,ratfac,riemann,trace] [christof,depends,determinant,diag_matrix,diff,exp,gcd,invert,load,matrix,ratfac,riemann] [christof,depends,diag_matrix,diff,exp,gcd,invert,load,matrix,ratfac,riemann,trace] [christof,depends,diag_matrix,diff,exp,gcd,invert,load,matrix,ratfac,riemann] [christof,depends,diag_matrix,diff,exp,gcd,load,matrix,ratfac,riemann] [christof,depends,diag_matrix,exp,gcd,lambda,load,matrix,ratfac,riemann,scurvature,sin] [christof,depends,diag_matrix,exp,gcd,load,matrix,ratfac,riemann,scurvature] [christof,depends,diag_matrix,exp,gcd,load,matrix,ratfac,riemann] [christof,depends,diag_matrix,gcd,load,matrix,ratfac,riemann,scurvature,sin] [christof,depends,diag_matrix,gcd,load,matrix,ratfac,riemann,scurvature] [christof,diag_matrix,exp,gcd,matrix,ratfac,sin] [christof,diag_matrix,gcd,load,matrix,ratfac,riemann,scurvature,sin] [christof,diag_matrix,gcd,load,matrix,ratfac,riemann,scurvature] [christof,diag_matrix,gcd,load,matrix,ratfac,riemann,sin] [christof,diag_matrix,gcd,load,matrix,ratfac,riemann] [christof,diag_matrix,gcd,load,matrix,ratfac,sin] [christof,diag_matrix,gcd,matrix,ratfac,sin] [christof,diag_matrix,matrix] [col,create_list,diag_matrix,genmatrix,ident,makelist,matrix,member,part,random,row,submatrix] [conjugate,diag_matrix,matrix,sqrt,transpose] [contract,delta,depends,diag_matrix,diff,exp,gcd,kron_delta,load,matrix,ratfac] [contract,depends,diag_matrix,diff,exp,gcd,load,matrix,ratfac] [cos,diag_matrix,eigenvalues,equal,matrix,ratsimp,sin,transpose,trigexpand,trigsimp] [cos,diag_matrix,eigenvalues,matrix,ratsimp,sin,transpose,trigsimp] [cos,diag_matrix,eigenvalues,matrix,sin,solve,transpose] [cos,diag_matrix,eigenvalues,matrix,sin,transpose] [cos,diag_matrix,equal,matrix,print,ratsimp,transpose,trigexpand,trigsimp] [cosh,diag_matrix,gcd,load,matrix,ratfac,riemann,scurvature,sinh] [depends,diag_matrix,einstein,gcd,load,matrix,ratfac,riemann,scurvature,sin] [depends,diag_matrix,gcd,load,matrix,ratfac,riemann,scurvature,sin] [diag_matrix,eigenvectors,matrix,transpose] [diag_matrix,gcd,load,matrix,ratfac] [diag_matrix,genmatrix,invert,lambda,matrix,transpose] [diag_matrix,genmatrix,invert,lambda,transpose] [diag_matrix,matrix,sin] [diag_matrix,matrix,transpose] [diag_matrix,matrix]

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