A = Matrix.New({{1,1,3},
                {1-1E-7,3,5},
                {3,5,1}})
val, funL, funR = Eigensystem(A)
print("The eigenvalues are\n",val)
print("The left  eigenfunctions are\n",funL)
print("The right eigenfunctions are\n",funR)
print("The matrix transformed to a diagonal matrix by its eigenfunctions is\n",Chop( Matrix.Conjugate(funL) * A * Matrix.Transpose(funR)) )

print("The left and right hand vectors are now only marginally different\n",Chop( Matrix.Conjugate(funL) * A * Matrix.Transpose(funL)) )