1. Angeles, J.: The Application of Dual Algebra to Kinematic Analysis. Computational Methods in Mechanical Systems. Springer, Berlin (1998)
2. Baksalary, J.K., Baksalary, O.M., Liu, X.: Further properties of the star, left-star, right-star, and minus partial orderings. Linear Algebra Appl. 375, 83–94 (2003)
3. Baksalary, O.M., Trenkler, G.: Core inverse of matrices. Linear Multilinear Algebra 58(6), 681–697 (2010)
4. Belzile, B., Angeles, J.: Reflections over the dual ring-applications to kinematic synthesis. J. Mech. Des. 141, 072302 (2019)
5. Belzile, B., Angeles, J.: Dual least squares and the characteristic length: applications to kinematic synthesis. In: Lovasz, E.C., Maniu, I., Doroftei, I., Ivanescu, M., Gruescu, C.M. (eds) New Advances in Mechanisms, Mechanical Transmissions and Robotics. MTM&Robotics 2020. Mechanisms and Machine Science, vol. 88, pp. 104–113. Springer, Cham (2020)
6. Coll, C., Herrero, A., Sánchez, E., Thome, N.: On the minus partial order in control systems. Appl. Math. Comput. 386, 125529 (2020)
7. Golubic, I., Marovt, J.: On some applications of matrix partial orders in statistics. Int. J. Manag. Knowl. Learn. 9(2), 223–235 (2020)
8. Hartwig, R.E.: How to partially order regular elements? Math. Japon. 25(1), 1–13 (1980)
9. Herrero, A., Thome, N.: Sharp partial order and linear autonomous systems. Appl. Math. Comput. 366, 124736 (2020)
10. Ling, C., He, H., Qi, L.: Singular values of dual quaternion matrices and their low-rank approximations. Numer. Funct. Anal. Optim. 43(12), 1423–1458 (2022)
11. Liu, Y., Ma, H.: Dual core generalized inverse of third-order dual tensor based on the T-product. Comput. Appl. Math. 41(8), 1–28 (2022)
12. Mitra, S.K., Bhimasankaram, P., Malik, S.B.: Matrix Partial Orders, Shorted Operators and Applications. World Scientific, Singapore (2010)
13. Pennestrì, E., Stefanelli, R.: Linear algebra and numerical algorithms using dual numbers. Multibody Syst. Dyn. 18(3), 323–344 (2007)
14. Pennestrì, E., Valentini, P.P., de Falco, D.: The Moore-Penrose dual generalized inverse matrix with application to kinematic synthesis of spatial linkages. J. Mech. Des. 140, 102303 (2018)
15. Penrose, R.: A generalized inverse for matrices. Math. Proc. Camb. Philos. Soc. 51(3), 406–413 (1955)
16. Qi, L.: Standard dual quaternion optimization and its applications in hand-eye calibration and SLAM. Commun. Appl. Math. Comput. (2022). https:// doi. org/ 10. 1007/ s42967- 022- 00213-1
17. Qi, L., Ling, C., Yan, H.: Dual quaternions and dual quaternion vectors. Commun. Appl. Math. Comput. 4, 1494–1508 (2022)
18. Qi, L., Luo, Z., Wang, Q.W., Zhang, X.Z.: Quaternion matrix optimization: motivation and analysis. J. Optim. Theory Appl. 193(1), 621–648 (2022)
19. Udwadia, F.E.: Dual generalized inverses and their use in solving systems of linear dual equations. Mech. Mach. Theory 156, 104158 (2021)
20. Udwadia, F.E.: When does a dual matrix have a dual generalized inverse? Symmetry 13(8), 1386 (2021)
21. Udwadia, F.E., Pennestri, E., de Falco, D.: Do all dual matrices have dual Moore-Penrose generalized inverses? Mech. Mach. Theory 151, 103878 (2020)
22. Wang, H.: Characterizations and properties of the MPDGI and DMPGI. Mech. Mach. Theory 158, 104212 (2021)
23. Zhong, J., Zhang, Y.: Dual group inverses of dual matrices and their applications in solving systems of linear dual equations. AIMS Math. 7(5), 7606–7624 (2022) |
