Description
The resulting matrix is over
CC, and contains the eigenvectors of
M. The lapack library is used to compute eigenvectors of real and complex matrices.
Recall that if
v is a non-zero 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
|