Abstract
To extend the concepts of the DMP, MPD and CMP inverses and solve several types of systems of equations, we define three new kinds of square matrices, called the index-MP, MP-index and MP-index-MP matrices. We prove several characterizations for new classes of matrices and their relations with significant generalized inverses. Several types of representations for these new matrices are established. We define new binary relations applying index-MP, MP-index and MP-index-MP matrices and we show that these relations are partial orders on the set including square matrices of index one.
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