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We introduce a new majorization order for classes (sets) of matrices which generalizes several existing notions of matrix majorization. Roughly, the notion says that every matrix in one class is majorized by some matrix in the other class. The motivation to study this majorization concept comes from mathematical statistics and involves the information content in experiments. This connection is briefly described. We investigate properties of this new order both of algebraic and geometric character. In particular, we establish results on so-called minimal cover classes with respect to the introduced majorization.

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