I m using the ComplexEigenSolver to find the eigenvalues and the eigenvectors of a non-symmetrical matrix.
In order to check whether the result make scene I use the ces.eigenvectors() * ces.eigenvalues().asDiagonal() * ces.eigenvectors().inverse()
and compare it with my matrix.
I found that it is really precise for most of the values but for some values there are differences.For example, some of the values of my matrix are (0,0) but from the product of ces.eigenvectors() * ces.eigenvalues().asDiagonal() * ces.eigenvectors().inverse() I get (0.893,0.692).Also, other values of my matrix are (0.5,0) or (0.125,0) and from the product I get (0,0).I should, finally,mention that most of the values of my matrix are 10^14 or 10^13.
Is there a way to improve the precision of the eigenvectors?The eigenvalues seem to be very good but it is not easy to be sure.
I m sorry for asking so many questions but my results aren't correct and I have to question every single part of my code to find the mistake.