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Apr 14, 2022 at 10:29 comment added Ryan Budney @DenisSerre: Well, the argument gives a little more than what was stated. The Jordan forms gives a stratification of the space of matrices, with matrices having repeated roots being of positive codimension. The stratification can be written in the language of Grassman manifolds and associated flag manifolds. I ?imagine? someone has described this but I don't know this end of the literature very well.
Apr 14, 2022 at 9:48 comment added Denis Serre This does not answer the question, since it proves only that the inetrior of the set of Hermitian matrices with repeated eigenvalues is void.
Apr 14, 2022 at 1:16 history answered Ryan Budney CC BY-SA 4.0