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Quaternion Two-Sided Matrix Equations with Specific Constraints

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Matrix and Operator Equations and Applications

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Abstract

This chapter is devoted to the survey of quaternion restricted two-sided matrix equation AXB = D and approximation problems related with it. Unique solutions to the considered approximation matrix problems and the restricted quaternion two-sided matrix equations with specific constraints are expressed in terms of the core-EP inverse and the dual core-EP inverse, the MPCEP and ∗CEPMP inverses, and the DMP and MPD inverses. The MPCEP-∗CEPMP inverses and the DMP-MPD inverses are generalized inverses obtained by combining the Moore-Penrose (MP-)inverse with the core-EP (CEP-)inverse and the MP-inverse with the Drazin (D-)inverse, respectively. Several particular cases of these equations and approximation matrix problems are presented too. Cramer’s rules for solving these constrained quaternion matrix equations and approximation matrix problems with their particular cases are developed by using of noncommutative row-column determinants. As a consequence, Cramer’s rules for solving these constrained matrix equations with complex matrices are derived as well. Numerical examples are given to illustrate gained results.

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Acknowledgements

Ivan I. Kyrchei thanks the Erwin Schrödinger Institute for Mathematics and Physics (ESI) at the University of Vienna for the support given by the Special Research Fellowship Programme for Ukrainian Scientists. Dijana Mosić and Predrag Stanimirović are supported from the Ministry of Education, Science and Technological Development, Republic of Serbia, Grants 451-03-47/2023-01/200124. Predrag S. Stanimirović is supported by the Science Fund of the Republic of Serbia (No. 7750185, Quantitative Automata Models: Fundamental Problems and Applications – QUAM).

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  1. Pidstryhach Institute for Applied Problems of Mechanics and Mathematics of NAS of Ukraine, L’viv, Ukraine

    Ivan I. Kyrchei

  2. Faculty of Sciences and Mathematics, University of Niš, Niš, Serbia

    Dijana Mosić & Predrag S. Stanimirović

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  1. Ivan I. Kyrchei
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  2. Dijana Mosić
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  1. Department of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran

    Mohammad Sal Moslehian

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Kyrchei, I.I., Mosić, D., Stanimirović, P.S. (2023). Quaternion Two-Sided Matrix Equations with Specific Constraints. In: Moslehian, M.S. (eds) Matrix and Operator Equations and Applications. Mathematics Online First Collections. Springer, Cham. https://doi.org/10.1007/16618_2023_45

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