# eigenvalues -- find eigenvalues of a matrix

## Synopsis

• Usage:
eigenvalues M
• Inputs:
• Optional inputs:
• Hermitian => ..., default value false, Hermitian=>true means assume the matrix is symmetric or Hermitian
• Outputs:
• , 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 library is used to compute eigenvectors of real and complex matrices.

## Caveat

The eigenvalues are approximate.