Inverse Operator over Index Matrices

Index matrices are an extension of the ordinary matrices with explicitly assigned index sets on both their rows and columns, forming an advanced mathematical structure used for specialized data modeling and problem-solving. In the present paper, a new operator, called “Inverse” operator, is defined over hierarchical index matrices with a description of its software implementation. This operator has no analogue in the classical theory of matrices. Its application allows various restructuring of datasets with multiple criteria, in order to outline data stratifications in the best possible way serving the particular decision maker’s needs. As an illustrative example for the new operator, a dataset of the recorded blood donors in Bulgaria is provided, with discussions of the different stratifications and perspectives in which the dataset can be rearranged using the “Inverse” operator.