octave:1> A=[5,4,1,1;4,5,1,1;1,1,4,2;1,1,2,4];
octave:2> [V,D] = eig(A);
octave:3> V
V =

    7.0711e-01   -1.6462e-16    3.1623e-01    6.3246e-01
   -7.0711e-01   -5.7067e-17    3.1623e-01    6.3246e-01
    2.2135e-16    7.0711e-01   -6.3246e-01    3.1623e-01
   -8.5465e-17   -7.0711e-01   -6.3246e-01    3.1623e-01

octave:4> D
D =

   1.00000   0.00000   0.00000   0.00000
   0.00000   2.00000   0.00000   0.00000
   0.00000   0.00000   5.00000   0.00000
   0.00000   0.00000   0.00000  10.00000

octave:5>