# A name for matrices with only simple eigenvalues?

I am constantly working with hermitian matrices without multiplicity in their spectrum. Since this hypothesis appear in several important problems, for instance perturbation theory, I looked in the literature for an accepted terminology but found nothing. Does anyone know a reference where these matrices, or their set, have been given a name ? I am considering calling them "simple matrices" but it is a bit ambiguous...

• I don't know of any established terminology but surely `simple' is a candidate for the most over-used adjective in mathematics. Anything else would be better!! – Nick Gill Oct 18 '13 at 7:31
• @NickGill: Anything? Let's try out randomlists.com/random-adjectives to test that. "Paltry matrices" or "upbeat matrices", perhaps? – Mark Meckes Oct 18 '13 at 8:02
• «Multiplicity-free» is a good name. – Mariano Suárez-Álvarez Oct 18 '13 at 8:03
• Another suggestion is separable, because the characteristic polynomial is separable. – Peter Mueller Oct 18 '13 at 11:25
• To me a simple matrix is one whose characteristic polynomial is irreducible. – Amritanshu Prasad Oct 18 '13 at 11:40

In the context of algebraic groups, these are the regular semisimple elements of $GL_n$. The "semisimple" part means diagonalizable, and the "regular" part means that the centralizer has dimension $n$. So you could call them regular semisimple.