A nonsymmetric, generalized eigenvalue problem is constructed from state-variable ensembles. The data-based eigenvalue problem is related to the state-variable formulation of linear multi-degree-of-freedom systems. The inverse-transpose of the eigenvector matrix from this eigenvalue problem converges to the state-variable modal eigenvectors, and the eigenvalues lead to estimates of frequencies and modal damping. The interpretation holds whether damping is modal or nonmodal, and without the need of input data. The method is illustrated on an eight degree-of-freedom mass-spring-dashpot example.

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