How about $M_n(\mathbb{R})^+ http://latex.mathoverflow.net/png?%24M%5Fn%28%5Cmathbb%7BR%7D%29%5E%2B$M_n(\mathbb{R})^+$? I have seen S^+ http://latex.mathoverflow.net/png?S%5E%2B$S^+$ or S_+ http://latex.mathoverflow.net/png?S%5F%2B$S_+$ used to denote the set of positive linear transformations in a set S http://latex.mathoverflow.net/png?S$S$ of linear transformations on an inner product space, but this was in the context of operator algebras.