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I am often designing math exams for students of engineering.

What I ask is the following:

*Can I choose any real 3x3 symmetric matrix with positive eigenvalues as a realistic matrix of inertia?*

Possibly, there are secret connections between the off-diagonal elements (if not zero) which I should have in mind...

I am not quite sure that the off-diagonal elements can be negative. Is it possible to have negative entries even on the diagonal line?

sfn17