# In mode superposition method, why do we select the dominant eigenvectors corresponding to small eigenvalues?

In my knowledge, we choose large singular values (same as eigenvalues in case of real symmetric and positive definite) for matrix order reduction. However, in the mode superposition method, why do we select the dominant eigenvectors corresponding to small eigenvalues?

I think it is physically rational to use the eigenvectors corresponding to small eigenvalues, but I can not understand mathematically.

To compare with eigendecomposition and singular value decomposition, the eigenvalue problem of interest is a static or dynamic problem where the mass matrix is an identity matrix.Therefore, I consider following equation:

$K\vec\phi=\lambda\vec\phi$,

where K is stiffness matrix and $\vec\phi$ is eigenvector corresponding to eigenvalue $\lambda$.

Can anyone help me here?

Best regards.

• What specific eigenvalue problem are we talking about? – Dylan May 24 '18 at 10:33
• @Dylan ; To compare with eigendecomposition and singular value decomposition, the eigenvalue problem of interest is a static or dynamic problem where the mass matrix is an identity matrix.Therefore, KΦ=λΦ where K is stiffness matrix and Φ is eigenvector corresponding to eigenvalue λ. – Cheolgyu Hyun May 24 '18 at 11:32
• Add that to the question, it'd provide more context – Dylan May 24 '18 at 11:56
• @Dylan Okay, thank you. – Cheolgyu Hyun May 24 '18 at 13:16