functions:EIGEN

check

 One way to check the result:

 e=EIGEN(m)
 n=vlen(m)[1]
 DO j = [1:n]
 ! these should be all zero (or close to zero)
   =m<>e[*,j]-e[j,n+1]*e[*,j]
 ENDDO 

example

 INPUT\MATRIX M 4 4
 2 -1 0 0
 -1 2 -1 0
 0 -1 2 -1
 0 0 -1 2
 E=EIGEN(M)
              | 0.37175  0.60150  0.60150 -0.37175  0.38197 |
              | 0.60150  0.37175 -0.37175  0.60150  1.38197 |
     Then E = | 0.60150 -0.37175 -0.37175 -0.60150  2.61803 |
              | 0.37175 -0.60150  0.60150  0.37175  3.61803 |

 The eigenvalues are E[*,5]
 The eigenvectors are E[*,j] for j = [1:4]