A new generalized inverse for rectangular matrices

摘要

The goal of this paper is to introduce a new generalized inverse, called the MMP-inverse along a matrix. Let C-mxn be the set of mxn complex matrices. Given any A. Cmxn and D. C-nxm, the matrix A is called MMP-invertible along D if there exists a matrix X is an element of C-nxm such that XAD = D and N( DAA(+)). subset of N (X). Such an X is called an MMP-inverse of A along D. Some characterizations of the MMP-inverse along a matrix are given by its range and null space. Also, the connection between the MMP-inverse along a matrix and other generalized inverses is investigated. Finally, the formula for the MMP-inverse of matrices is expressed.

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