Singular Manual: eigenvals

D.3.2.18 eigenvals

Procedure from library linalg.lib (see linalg_lib).

Usage:

eigenvals(M); matrix M

Assume:

eigenvalues of M in basefield

Return:

list l;
  ideal l[1];
    number l[1][i];  i-th eigenvalue of M
  intvec l[2];
    int l[2][i];  multiplicity of i-th eigenvalue of M

Example:

LIB "linalg.lib";
ring R=0,x,dp;
matrix M[3][3]=3,2,1,0,2,1,0,0,3;
print(M);
==> 3,2,1,
==> 0,2,1,
==> 0,0,3 
eigenvals(M);
==> [1]:
==>    _[1]=2
==>    _[2]=3
==> [2]:
==>    1,2