TITLE: Why is the multiset of eigenvalues called spectrum?
QUESTION [14 upvotes]: Somebody came to me and asked the following:

Why is the multiset of eigenvalues called spectrum?

I cannot find the reason anywhere.

REPLY [3 votes]: Newton introduced the word "spectrum" in sciences from 1666. The terminology of the eigen-elements of a matrix is fixed by Jordan in 1870 (in fact, for a while, mathematicians use "proper value" (Jordan) or "eigenvalue" (Hilbert)).
In 1907, functional analysis appears; in 1910, Weyl gives his definition of what would later be called a variant of the "essential spectrum".
Then comes the equivalence between the  Heisenberg's matricial mechanics and the Schrodinger's equation (1926). Yet, the word spectrum still does not exist in the sense that interests us.
Note that a spectrum (for its future standard definition) of a Banach operator may be discrete or continuous (as $\phi:f(x)\in C^0([0,1])\rightarrow xf(x)\in C^0([0,1]))$. Therefore,  the so called spectrum has some points in common with the spectrum of physicists. Moreover these two notions give each one a lot of information about the studied object. 
Anyway, in english, "spectrum" is used -for operators- from 1948. Since in finite dimension, the spectrum reduces to the set of eigenvalues, the word "spectre" is used in France -for the matrices- from 1964; on the other hand, "spectrum" is pronounced faster than "the set of eigenvalues"!!