Demonstrates properties of a generalized inverse in rectangular matrices, highlighting its use in constrained optimization problems.
We extend the concept of the m-weak group MP inverse of a square matrix to a rectangular matrix, called the W-weighted m-weak group MP inverse, which also unifies the W-weighted weak core inverse and W-weighted DMP inverse. Some properties, characterizations, and representations of this new generalized inverse are shown. Additionally, applications of the W-weighted m-weak group MP inverse are presented in solving a constrained optimization problem and a class of consistent matrix equations. Several numerical examples are proposed to illustrate some results given in the paper.
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Gao et al. (2026) studied this question.
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