**Disclaimer:** This might be an SE question, but I'm not quite sure...

Thanks in advance!

# Setup

So, it is known (see Proposition 5.2) that if $A + A^T$ is positive-definite then $A$ must be a $P$-matrix. Thus this gives a simple way for generating P-matrices (which are otherwise very complex objects, due to the "principal minors" conditions defining them)

# Question

What (if any ) interesting things can be said about matrices $A$ for which $A + A^T$ is p.d. ?

What are some interesting non-trivial ways for generating such matrices (i.e matrices for which $A + A^T$ is p.d) ?