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A note on the solvability for generalized Sylvester equations

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

In this paper, we give a new necessary and sufficient condition for the solvability of the system of generalized Sylvester real quaternion matrix equations \(A_{i}X_{i}+Y_{i}B_{i}+C_{i}ZD_{i} =E_{i}\), (\(i=1,2\)). Moreover, using the purely algebraic technique, we consider the solvability of the system of generalized Sylvester equations in a unital ring.

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Funding

The author is highly grateful to the referee for his/her valuable comments and suggestions which led to improvements of this paper. The research is supported by the National Natural Science Foundation of China (11901510), the National Natural Science Foundation of Jiangsu Province (BK20170589), China Postdoctoral Science Foundation Funded Project (2017M611920).

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Authors and Affiliations

  1. Faculty of Science, Bengbu University, Bengbu, 233030, People’s Republic of China

    Huaxi Chen

  2. School of Mathematics, Yangzhou University, Yangzhou, 225002, People’s Republic of China

    Long Wang & Tingting Li

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  1. Huaxi Chen
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  2. Long Wang
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  3. Tingting Li
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Correspondence to Tingting Li.

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Chen, H., Wang, L. & Li, T. A note on the solvability for generalized Sylvester equations. RACSAM 115, 64 (2021). https://doi.org/10.1007/s13398-020-00957-6

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  • DOI: https://doi.org/10.1007/s13398-020-00957-6

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