A matrix has its design in the same sense as a die. The design is engraved convex into the matrix, which is used to create punches. The matrix step was developed in the 17th century for two main reasons. The original design in the matrix could be better preserved, as a single matrix could be used to make several punches. Second, it made easier the addition of secondary details such as the legend, otherwise a difficult task.
In a similar sense, a matrix is the term for a mould or die used for making a wax, metal or clay seal intended for purposes of authentication.