# Orthonormalization of eigenamplitudes

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.