Why is the multiset of eigenvalues called spectrum?

Question

Somebody came to me and asked the following:

Why is the multiset of eigenvalues called spectrum?

I cannot find the reason anywhere.

Answer 1

Not too surprisingly, it seems to come from physics. I'm sure others here can provide much better detail, but here is a quote from a small article called "Favorite Eigenvalue Problems" in SIAM News, Volume 44, Number 10, December 2011 by Nick Trefethen:

Eigenvalues played a role in a great coincidence of scientific history. Physicists saw spectral lines in the light from stars; indeed, an unfamiliar line led to the discovery of helium. Later, Hilbert defined spectra of operators. Not until Schrödinger, decades on, was it understood that physicists’ spectra were exactly a case of mathematicians’ spectra, with each line corresponding to the difference in energy of two eigenstates. And it was these same spectral lines that led to the discovery of the red shift and the expanding universe.