Program to find the eigenvalues and eigenvectors of a real square matrix A

The number of matrix rows = 3
a(1,1) = 1
a(1,2) = 2
a(1,3) = 3
a(2,1) = 2
a(2,2) = 4
a(2,3) = 7
a(3,1) = 1
a(3,2) = 1
a(3,3) = 2
Solution decimal places = 20 fixed-point

                        Distinct Eigenvalues
                                                             Apparent
No.          Real Part               Imaginary Part        multiplicity
 1    7.02029036453021677394~    0.00000000000000000000~         1
 2   -0.01014518226510838697~    0.37728149422028935082~         1
 3   -0.01014518226510838697~   -0.37728149422028935082~         1

                        Eigenvectors
All vectors displayed have a 1 component of largest magnitude

Eigenvalue No. 1 eigenvector
Component           Real Part                   Imag Part
     1       0.47901739646783575000~     0.00000000000000000000~ 
     2       1.00000000000000000000      0.00000000000000000000  
     3       0.29460793879922075342~     0.00000000000000000000~ 

Eigenvalue No. 2 eigenvector
Component           Real Part                   Imag Part
     1       0.10831738872260386413~    -0.78969991199615350637~ 
     2       1.00000000000000000000      0.00000000000000000000  
     3      -0.60382570853004515932~     0.27952590260179948051~ 

Eigenvalue No. 3 eigenvector
Component           Real Part                   Imag Part
     1       0.10831738872260386413~     0.78969991199615350637~ 
     2       1.00000000000000000000      0.00000000000000000000  
     3      -0.60382570853004515932~    -0.27952590260179948051~ 

                        Eigenvalue Matrix (Complex)
 7.02029036453021677394~    0.00000000000000000000~        
-0.01014518226510838697~    0.37728149422028935082~        
-0.01014518226510838697~   -0.37728149422028935082~        

Eigenvector Matrix (Real) (Transposed)
               0.47901739646783575000~        1.00000000000000000000         0.29460793879922075342~    
               0.10831738872260386413~        1.00000000000000000000        -0.60382570853004515932~    
               0.10831738872260386413~        1.00000000000000000000        -0.60382570853004515932~    

Eigenvector Matrix (Imaginary) (Transposed)
               0.00000000000000000000~        0.00000000000000000000         0.00000000000000000000~    
              -0.78969991199615350637~        0.00000000000000000000         0.27952590260179948051~    
               0.78969991199615350637~        0.00000000000000000000        -0.27952590260179948051~