eigen_power.c running, find largest eigenvalue 
initial matrix A1 n=3
  3.00000000   -1.00000000    0.00000000  
 -2.00000000    4.00000000   -3.00000000  
  0.00000000   -1.00000000    1.00000000  

eigenvalue=  5.47735369, error=6.58907e-07, eigenvector is 
 -0.40365719    1.00000000   -0.22334619  

check eigenvalue and eigenvector 
determinant should be zero = -2.2018e-05 
eigenvector errors 
  0.00000163   -0.00000074   -0.00000011  


initial matrix A2 n=3
  6.00000000   12.00000000   19.00000000  
 -9.00000000  -20.00000000  -33.00000000  
  4.00000000    9.00000000   15.00000000  

eigenvalue=  1.03537339, error=0.00488069, eigenvector is 
 -0.50325380    1.00000000   -0.49837310  

check eigenvalue and eigenvector 
determinant should be zero = -0.00254681 
eigenvector errors 
  0.03244387   -0.05977686    0.02739053  


invert A1 and find the smallest eigenvalue 
initial matrix A3 n=3
  1.00000000    1.00000000    3.00000000  
  2.00000000    3.00000000    9.00000000  
  2.00000000    3.00000000   10.00000000  

eigenvalue= 13.40894701, error=7.64984e-07, eigenvector is 
  0.31633818    0.92542293    1.00000000  

check eigenvalue and eigenvector 
determinant should be zero = -0.00033062 
eigenvector errors 
 -0.00000076   -0.00000186   -0.00000186  

The smallest eigenvalue of A1 is 1 over, =   0.07457707 

check eigenvalue of original A1 
determinant should be zero = 1.37134e-07