[light_hue_1]

And you learn literally zero about a candidate's ability to understand when and why things work by asking questions about eigenvectors. Someone can understand what an eigenvector is and still not have any clue about how you figure out a system is working, why it's working, what is likely to happen in production, how you test the limits of your method's ability to generalize, how you take an real problem and find something that you can productively use ML on, etc.

People say things like "you need to know how it works" but "it" doesn't work using your knowledge of eigenvectors. If you want to test how "it" works, test that, literally. Put up a model on the board and a dataset. Ask people about what might happen when you apply one to the other. What changes they would make in response to changes in the data. What they would do in response to the following training curves, budget limitations, etc.

These interviews are terrible and they select for people that regurgitate facts.

[uoaei]

The "trivia" tests, when used (IMO) correctly, are not for testing whether or not the candidate recognizes the term and can regurgitate a definition. I prefer to listen to how they phrase their response to get a sense of the intuition behind the understanding of the concept as well as how it may fit in to a larger mathematical framework (i.e. their internal model for mathematical analysis).

I am not looking for someone to answer the question correctly, but to answer the question in a way that demonstrates deeper insights, which helps immensely in research settings as re-using properties of mathematical constructs in novel ways is often how theory and practice both are advanced.

I would be much less interested in someone giving a precise definition of eigenvalues than to describe them in such a way that they understand e.g. what can be deduced about an operator when one of its eigenvalues is zero.