{
   const Int_t NBINS = 3;
   TMatrix tcovmat(NBINS,NBINS);

   for (Int_t i=0;i<NBINS;i++) {
     for (Int_t j=0;j<=i;j++) {
        //... blah blah computing the elements of the matrix...
       const Float_t aaa = (i == j) ? 1.0 : 0.0;
       tcovmat[i][j]=aaa;
       tcovmat[j][i]=aaa; //symmetric
     }
   }
   TVector eigenvalues;
   TMatrix eigenvectors = tcovmat.EigenVectors(eigenvalues);

   eigenvectors.Print();
   eigenvalues.Print();
}