Resolution of the Generalized Eigenvalue Problem for symmetric matrices

The analysis of dynamical systems with multiple degrees of freedom leads to the following eigenvalue problem:

(K - λ M) u = 0.

The program calculates the eigenvalues ββλ_{i} and corresponding eigenvectors u_{i}.

For dynamical systems of multiple degrees of freedom K is the stiffness matrix and M is the mass matrix.
The eigenfrequencies ω_{i} of the modes of vibration can be calculated by means of ω^{2} = λ.
Required is that matrices M and Kare symmetric. In addition M must be positive definite
and the matrix of K must be positive semi-definite.