1
vote
1answer
48 views

Is the trace of a Lyaponov transform of a semistable matrix always nonpositive?

Let $A$ be a semistable real matrix (i.e. the real parts of all the eigenvalues of $A$ are nonnegative). Let $P$ be a positive definite matrix. Is it always true that $\text{trace}{A^{T}P+PA} ...