Definition of simple spectrum

Question

From the book "Spinning Tops" by Audin, given Lax equation $[A_{\lambda},B_{\lambda}]$ where $\lambda$ is a parameter (so called spectral parameter), she claims that we have spectral curve $P(\lambda,\nu)=0$ where $P(\lambda,\nu)$ is a characteristic polynomial of $A_{\lambda}$. Then, she talks about when $A_{\lambda}$ has a simple spectrum. I tried to look for definition of it, but I couldn't find it. Can you please tell me what does it mean for a spectrum to be simple?

Answer 1

I suspect she means that the eigenvalues are all simple, i.e. the characteristic polynomial has no multiple roots.