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2.718281828459
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Hello. I am working on a project with a double pendulum and I am currently looking for the normal mode frequencies. I don't think that's too important to answer my question, but in the derivation I hit a point that look like this:[itex](K-M\omega^{2})\alpha=0.[/itex] Here, K and M are 2x2 square matrices. I want to solve for the eigenvalue here, but this doesn't follow the form that I normally have with eigenvector equations. If I rearrange this, I get [itex]K\alpha=M\omega^{2}\alpha[/itex] which has a matrix on each side. Naturally I thought to multiply by the inverse of M on both sides to get [itex]M^{-1}K\alpha=\omega^{2}\alpha.[/itex] However, this didn't give the correct result. Why not? How should it be done?