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Cramer’s Rule for the General Solution to a Restricted System of Quaternion Matrix Equations

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Abstract

In this paper, we mainly study the Cramer’s rule for the general solution to the restricted system of quaternion matrix equations

and the Cramer’s rule for the general solution to the restricted generalized Sylvester quaternion matrix equation

$$\begin{aligned} AXB+CYD=E,\text { }\mathcal {R}_{r}\left( X\right) \subset T_{1} ,\mathcal {N}_{r}\left( X\right) \supset S_{1},\mathcal {R}_{r}\left( Y\right) \subset T_{2},\mathcal {N}_{r}\left( Y\right) \supset S_{2} \end{aligned}$$

respectively. The findings of this paper extend some known results in the literature.

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Authors and Affiliations

  1. School of Mathematics and Information Sciences, Weifang University, Weifang, 261061, People’s Republic of China

    Guang-Jing Song

  2. Department of Mathematics, East China University of Science and Technology, Shanghai, 200237, People’s Republic of China

    Shao-Wen Yu

Authors
  1. Guang-Jing Song
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  2. Shao-Wen Yu
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Correspondence to Shao-Wen Yu.

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Pierre-Philippe Dechant

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This research was supported by Shanghai Natural Science Foundation (17ZR1407800), The National Science Foundation of China (11601328).

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Song, GJ., Yu, SW. Cramer’s Rule for the General Solution to a Restricted System of Quaternion Matrix Equations. Adv. Appl. Clifford Algebras 29, 91 (2019). https://doi.org/10.1007/s00006-019-1000-1

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