Abstract: In this paper,we discuss the problem of estimating a common mean parametric matrix relative to matrix loss. We give six different optimality criterias and prove them to be identical in the class of homogenous linear estimates and get a necessary and sufficient codition for their common admissible estimate. However in the class of homogenous linear estimates,it will not be true any longer. but we can divide those criteris into two idetical subclasses and give each subclass a necessary and sufficiet condition for their common admissible estimate respectively.