Additive results of the dual Moore--Penrose generalized inverse with an application to rigid-body motion estimation
Year: 2026
Type: preprint
Abstract: We derive explicit formulas for the dual Moore--Penrose generalized inverse (DMPGI) of dual complex matrix sums under some conditions. We first express the DMPGI of a matrix partitioned into column blocks in terms of these blocks and associated projectors, and then derive two formulas for matrix sums. Two examples illustrate the results. We further apply the formulas to rigid-body motion estimation with two observation points subject to a first-order perturbation of their positions that preserves the rank-deficient observation geometry. The DMPGI recovers the observable motion components from the velocity data.
Source: arXiv (Cornell University)
Authors: Zhao, Yue, Zhang, Daochang
Institutions: Georgia State University, Changchun Normal University
Language: English
Topic: Matrix Theory and Algorithms
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Awards: G2759900957, G3387435490, G4284525095
OpenAlex ID: W7221786411