General Eigenvalue Problem

The general eigenvalue problem can be expressed as the matrix equation.
$$[K][\phi]=[M][\phi][\lambda]$$
Where \([K]\) and \([M]\) are nxn positive definite symmetric matrices. \([\phi]\) is an nxp matrix that contains \(p\) eigenvectors, and \([\lambda]\) is a p x p matrix containing p eigenvalues. When describing structural analysis problems \([K]\) is the stiffness matrix and \([M]\) is the mass matrix. This problem can be solved with basic matrix methods such as the Power, QR, or Arnoldi Methods.

[[4-Story Building Shear]] – formulated as a general eigenvalue problem
[[Power Method]] – method for solving eigenvalues
Modal Participation Analysis – uses the general eigenvalue problem for vibration analysis.
[[Arnoldi Method]]
[[Advantages of the QR algorithm]] – solves for all eigenvalues
[[Wing Rock]] – can be represented as a general eigenvalue problem

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