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PreprintarXiv licencearXiv

Additive results of the dual Moore--Penrose generalized inverse with an application to rigid-body motion estimation

  • Yup Zhao
  • Daochang Zhang
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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.

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Cite

BibTeXRIS
BibTeX
@misc{zhao2026additive,
  title = {{Additive results of the dual Moore--Penrose generalized inverse with an application to rigid-body motion estimation}},
  author = {Yup Zhao and Daochang Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.16852},
  eprint = {2610.16852},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.16852},
}
RIS
TY  - UNPB
TI  - Additive results of the dual Moore--Penrose generalized inverse with an application to rigid-body motion estimation
AU  - Yup Zhao
AU  - Daochang Zhang
PY  - 2026
DA  - 2026/10/12
PB  - arXiv
DO  - 10.48550/arxiv.2610.16852
UR  - https://arxiv.org/abs/2610.16852
AB  - 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.
ER  -