eigenvalues -- find eigenvalues of a matrix

Synopsis

Usage:

eigenvalues M
Inputs:
- M, a matrix, or a MutableMatrix over RR or CC, which is a square n by n matrix
Optional inputs:
- Hermitian => ..., default value false, Hermitian=>true means assume the matrix is symmetric or Hermitian
Outputs:
- a vertical list, a list of the eigenvalues of M

Description

In this example we compute the eigenvalues of a matrix and display their classes.

i1 : M = matrix {{1,2}, {5,7}}

o1 = | 1 2 |
     | 5 7 |

              2       2
o1 : Matrix ZZ  <-- ZZ

i2 : eigenvalues M

o2 = {-.358899}
     {8.3589  }

o2 : VerticalList

i3 : class \ oo

o3 = {CC}
     {CC}

o3 : VerticalList

If the matrix is symmetric (over RR) or Hermitian (over CC), this information may be provided as an optional argument Hermitian=>true, so the resulting eigenvalues will be in RR, not CC.

i4 : M = matrix {{1,2}, {2,1}}

o4 = | 1 2 |
     | 2 1 |

              2       2
o4 : Matrix ZZ  <-- ZZ

i5 : eigenvalues(M, Hermitian=>true)

o5 = {-1}
     {3 }

o5 : VerticalList

i6 : class \ oo

o6 = {RR}
     {RR}

o6 : VerticalList

The lapack and eigen libraries are used to compute eigenvectors of real and complex matrices.

Caveat

The eigenvalues are approximate.

Ways to use eigenvalues :

eigenvalues(Matrix)
eigenvalues(MutableMatrix)

For the programmer