Build Vorticity Matrix for Markov chain

I have a markov chain with $ Q(u,v)$ as transition probability matrix and $ \pi(u)$ as stationary distribution. The dimension of matrix $ Q$ is $ nxn$ and vector $ \pi$ is $ 1xn$ .

I need to build a vorticity matrix $ \Gamma (u,v)$ of dimension $ nxn$ which has below properties

1. $ \Gamma$ is skew symmetric matrix i.e, $ $ \Gamma (u,v) = -\Gamma (v,u)$ $

2. Row sum of $ \Gamma$ is zero for every row i.e, $ $ \sum_v \Gamma (u,v) = 0$ $

3. Third property is, $ $ \Gamma(u,v) \geq -\pi (v)Q(v,u) $ $

How to build vorticity matrix $ \Gamma (u,v)$ which satisfies above three properties?

NOTE: Transition probability matrix $ P$ , and stationary distribution $ \pi$ has below properties

Row sum of $ P$ is one for each row, $ $ \sum_v P(u,v)=1$ $ $ \pi$ is probability distribution hence, $ $ \sum_v \pi(v) = 1$ $ Stationary distribution condition for $ \pi$ , $ $ \sum_u \pi(u) P(u,v) = \pi(v)$ $

The post Build Vorticity Matrix for Markov chain appeared first on 100% Private Proxies - Fast, Anonymous, Quality, Unlimited USA Private Proxy!.