On 2MP-, MP2-, and CMP2-inverses in \(\ast\)-rings
Janko Marovt, Dijana Mosić · Glasnik Matematicki · 2025
The notions of a 2MP-inverse, a MP2-inverse, and a C2MP-inverse are extended from the set of all \(m\times n\) complex matrices to the set \(\mathcal{R}^{\dagger}\) of all Moore-Penrose invertible elements in a unital \(\ast \)-ring \(\mathcal{R}\). We study properties of these hybrid generalized inverses and thus generalize some known results. We apply the \((b,c)\)-inverse of \(a\in \mathcal{R}^{\dagger}\) to determine a special case of a 2MP- or MP2-inverse of \(a\) and then use these inverses to solve certain equations which lead to least-squares solutions and the normal equation.