I cannot explain this eigenvalue problem. Both matrices are positive definite and symmetric, but some solutions are complex.
But if it is matrices lower order, solutions are real. As I increase the number of order the matrices, I got more and more complex solutions (and in same time matrices are positive definite and symmetric.) What is the problem? I try to increase precision, but nothing.
From here you can copy and paste in Mathematica worksheet to see.
http://pastebin.com/raw.php?i=hM6DBVk5
Regards