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 ​​λi and corresponding eigenvectors ui.

For dynamical systems of multiple degrees of freedom K is the stiffness matrix and M is the mass matrix.
The eigenfrequencies ωi of the modes of vibration can be calculated by means of ω2 = λ.
Required is that matrices M and K are symmetric. In addition M must be positive definite and the matrix of K must be positive semi-definite.

Number of rows




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