- #1

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## Summary:

- What is the geometry/topology of the set of defective matrices

## Main Question or Discussion Point

Let me start by saying that my question will be somewhat vague by mathematical standards. I'm not a mathematician! I'm looking for some intuition about how defective matrices are distributed in the space of all matrices. I understand that they are rare and in some sense discontinuous - matrices switch from being non-normal to defective with an infinitesimal change of parameters. But for example, do they form some kind of manifold? Does the set of defective matrices have measure zero? Are there any interesting known properties about the topology or geometry of the set of defective matrices?

Thanks for your thoughts.

Thanks for your thoughts.