Assuming $(-\omega^2 \hat m + \hat k)\vec{a}=0$ where $\vec a$ is the eigenamplitude of the eigenfrequency $\omega$ , $\hat m$ is the mass matrix and $\hat k$ is the matrix of the potential constants.

So to orthonormalize $\vec a$ it has to fulfil $\vec a^T \hat m \vec a=1$.

I wonder why this is. What kind of orthonormalization is this. Where does it come from. Because using Gram-Schmidt on the matrix of eigenamplitudes doesn't lead to the same result.

I hope my question is clear but feel free to correct me on anything.


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