A =    
 
    2.  - 1.    1.    4.  
  - 1.    3.    1.    2.  
    1.    1.    5.  - 3.  
    4.    2.  - 3.    6.  
 
 Ai =    
 
    2.      - 1.4142    1.D-16    4.      
  - 1.4142    3.      - 1.        3.5355  
    1.D-16  - 1.        5.      - 0.7071  
    4.        3.5355  - 0.7071    6.      
 
 X =    
 
    1.    0.        0.        0.  
    0.    0.7071    0.7071    0.  
    0.  - 0.7071    0.7071    0.  
    0.    0.        0.        1.  
 
 Theta =    
 
    0.7854  
 
 Ai =    
 
    2.      - 4.2426    1.D-16  - 2.D-16  
  - 4.2426    3.4444    0.3333  - 3.6927  
    1.D-16    0.3333    5.      - 1.1785  
  - 2.D-16  - 3.6927  - 1.1785    5.5556  
 
 X =    
 
    1.    0.        0.    0.      
    0.    0.3333    0.    0.9428  
    0.    0.        1.    0.      
    0.  - 0.9428    0.    0.3333  
 
 Theta =    
 
    1.231  
 
 Ai =    
 
    2.      - 4.2426    2.D-16    9.D-17  
  - 4.2426    3.4444    3.7077  - 2.D-16  
    2.D-16    3.7077    5.7621    1.1097  
    9.D-17  - 3.D-16    1.1097    4.7934  
 
 X =    
 
    1.    0.    0.        0.      
    0.    1.    0.        0.      
    0.    0.    0.0899    0.9960  
    0.    0.  - 0.9960    0.0899  
 
 Theta =    
 
    1.4808  
 
 Reduced A1 to trigonal matrix is :    
 
    2.      - 4.2426    2.D-16    9.D-17  
  - 4.2426    3.4444    3.7077  - 2.D-16  
    2.D-16    3.7077    5.7621    1.1097  
    9.D-17  - 3.D-16    1.1097    4.7934    
 e =    
 
    1.  
    0.  
    0.  
 
 x =    
 
  - 1.  
    1.  
    4.  
 
 k =    
 
    4.2426  
 
 u =    
 
  - 5.2426  
    1.      
    4.      
 
 Householder Matrix :    
 
  - 0.2357    0.2357    0.9428  
    0.2357    0.9550  - 0.1798  
    0.9428  - 0.1798    0.2807