Math Kernel Library MKL

I want to use Intel Math Kernel Library (MKL) to calculate the bifurcation loads and modes in my custom FE program. MKL has many algorithms and I want to use the most efficient one.
Basically, I need to find a few eigenvalues lambda_i and eigenvectors u_i for the problem
KG * u = lambda * KS * u
where KG is the stiffness matrix and KS is the geometric stiffness matrix, also called stress-displacement matrix.
Is KG supposed to be positive definite?
When finding the vibration frequencies and modes, the equation is the same with KS beign the mass matrix, which is positive definite, but for buckling, is KS supposed to be +definite as well?