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Macaulay2Doc :: eigenvalues

eigenvalues -- find eigenvalues of a matrix

Synopsis

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 library is used to compute eigenvectors of real and complex matrices.

Caveat

The eigenvalues are approximate.

See also

Ways to use eigenvalues :

For the programmer

The object eigenvalues is a method function with options.