For the positive definite imaginary part, I am still a bit confused. The imaginary part of does not even seem to be Hermitian. But I think I see how to get the conclusion that follows anyway: The eigenvalues above have positive imaginary part . Using the fact that has an orthogonal eigenbasis, you can now calculate that the has a nonnegative imaginary part for any .

Is this what it means for the imaginary part of $\latex R$ to be positive definite?

]]>For the positive definite imaginary part, I am still a bit confused. The imaginary part of does not even seem to be Hermitian. But I think I see how to get the conclusion that follows anyway: The eigenvalues above have positive imaginary part . Using the fact that has an orthogonal eigenbasis, you can now calculate that the has a nonnegative imaginary part for any .

Is this what it means for the imaginary part of $\latex R$ to be positive definite?

]]>$latex[x^2 + \phi]$ ]]>

What happens if instead of both properties, just one of them is forbidden? For example, if we forbid three sets in our family, so that ?

]]>$x^2 + x – 1 = 0$ ]]>