Resolution of the Generalized Eigenvalue Problem for symmetric matrices

Here the following problem eigenvalue problem is solved:

(K - λ M) u = 0.

The program calculates the eigenvalues ββλ_{i} and their eigenvectors u_{i}.
For dynamical systems of multiple degrees of freedom K is the stiffness matrix and M is the mass matrix.

The eigenfrequencies of the modes of vibration can be calculated by means of ω^{2} = λ.
Required is that matrices M and Kare symmetric. Also M must be positive definite
and the matrix of K must be positive semi-definite.