Does the word "spectrum" in linear algebra have different meanings?

Question

I'm reading several papers that refer to the spectrum as the set of all possible eigenvalues of a matrix, i.e., counting multiplicity, so that a list such as $\sigma = (\alpha_1, ... \alpha_n, 0, 0, 0,...,0)$ can be the spectrum of some matrix.

But I had learned in my linear algebra courses that the spectrum is the set of distinct eigenvalues.

Who is right?

Does the spectrum have different meanings?

This difference is not a triviality, for the paper that I am trying to work on - for example, adding more zeroes to the list changes the problem; adding more zeroes can increase the solvability of the problem.

So, I just want to make sure.

Thanks,

Answer 1

Spectrum is a subject in functional analysis rather than linear algebra. Its concept in functional analysis is more extended than eigenvalue. Eigenvalue is a special case of elements of spectrum. You can see functional analysis Rudin.