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"Every linear system is characterized by special inputs that are invariant to the system, i.e., inputs that are not altered (except for a multiplicative constant) upon passage through the system. These inputs are called the modes, or the eigenfunctions, of the system. The multiplicative constants are the eigenvalues; they are the attenuation or amplification factors of the modes."

What is the link between this definition and the eigenvalue problem determined by helmholtz equation?