# large eigenvalues with LAPACK

I have question about LAPACK. I calculate eigenvalues of a $16\times16$ Hermitian complex matrix with small entries by ZHEEV subroutine, but the size of eigenvalues are very large! May it possible?

Trace in the initial matrix is of the order 1E-17 and summation of eigenvalues is of the order of 1E-12. Info is "0" and work is large enough. When I try this program with small dimension eigenvalues is small.

Usually what kind of mistakes may cause this kind of problem?! Thanks for time you spent

• Welcome to Scicomp Exchange. Where the matrix comes from? and what is the condition number of your matrix? – nicoguaro Apr 20 '15 at 19:58
• A quick way to get an idea of where your eigenvalues truly are is to use Gershgorin's circle theorem (en.wikipedia.org/wiki/Gershgorin_circle_theorem). – Juan M. Bello-Rivas Apr 20 '15 at 23:36
• Is the matrix positive definite? What is its norm? What is the condition number of the eigenvector matrix (which is a good measure to tell when an eigenproblem is ill-conditioned)? Could you please export the matrix with full precision and put it online for us to see, since it is so small? It could be a LAPACK bug, but let's rule out the other possibilities first. – Federico Poloni Apr 22 '15 at 7:31