Description
The resulting matrix is over
CC, and contains the eigenvectors of
M. The lapack and eigen libraries are used to compute eigenvectors of real and complex matrices.
Recall that if
v is a nonzero vector such that
Mv = av, for a scalar a, then
v is called an eigenvector corresponding to the eigenvalue
a.
i1 : M = matrix{{1, 2}, {5, 7}}
o1 =  1 2 
 5 7 
2 2
o1 : Matrix ZZ < ZZ

i2 : eigenvectors M
o2 = ({.358899},  .827138 .262266 )
{8.3589 }  .561999 .964996 
o2 : Sequence

If the matrix is symmetric (over
RR) or Hermitian (over
CC), this information should be provided as an optional argument
Hermitian=>true. In this case, the resulting eigenvalues will be returned as real numbers, and if
M is real, the matrix of eigenvectors will be real.
i3 : M = matrix {{1, 2}, {2, 1}}
o3 =  1 2 
 2 1 
2 2
o3 : Matrix ZZ < ZZ

i4 : (e,v) = eigenvectors(M, Hermitian=>true)
o4 = ({1},  .707107 .707107 )
{3 }  .707107 .707107 
o4 : Sequence

i5 : class \ e
o5 = {RR}
{RR}
o5 : VerticalList

i6 : v
o6 =  .707107 .707107 
 .707107 .707107 
2 2
o6 : Matrix RR < RR
53 53
