Definition

In the MH algorithm we use a proposal kernel which we define as $T(\cdot|\cdot)$ where $$$$\begin{align*} &T(\cdot|\cdot)\mbox{ is the transition matrix on }S_{i}\\\\ &T(y|x)\mbox{ is the one-step transition probability}\\\\ &T(\cdot|x)\mbox{ is a row in }T(\cdot|\cdot) \end{align*}$$$$