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The Real and Complex Hermitian Solutions to a System of Quaternion Matrix Equations with Applications

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  • Shao-Wen Yu

Abstract

We establish necessary and sufficient conditions for the existence of and the expressions for the general real and complex Hermitian solutions to the classical system of quaternion matrix equations ð ´ 1 ð ‘‹ = ð ¶ 1 , ð ‘‹ ð µ 1 = ð ¶ 2 , a n d ð ´ 3 ð ‘‹ ð ´ âˆ— 3 = ð ¶ 3 . Moreover, formulas of the maximal and minimal ranks of four real matrices ð ‘‹ 1 , ð ‘‹ 2 , ð ‘‹ 3 , and ð ‘‹ 4 in solution ð ‘‹ = ð ‘‹ 1 + ð ‘‹ 2 ð ‘– + ð ‘‹ 3 ð ‘— + ð ‘‹ 4 𠑘 to the system mentioned above are derived. As applications, we give necessary and sufficient conditions for the quaternion matrix equations ð ´ 1 ð ‘‹ = ð ¶ 1 , ð ‘‹ ð µ 1 = ð ¶ 2 , ð ´ 3 ð ‘‹ ð ´ âˆ— 3 = ð ¶ 3 , and ð ´ 4 ð ‘‹ ð ´ âˆ— 4 = ð ¶ 4 to have real and complex Hermitian solutions.

Suggested Citation

  • Shao-Wen Yu, 2012. "The Real and Complex Hermitian Solutions to a System of Quaternion Matrix Equations with Applications," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2012, pages 1-19, January.
    • Handle: RePEc:hin:jijmms:307036
    DOI: 10.1155/2012/307036
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    References listed on IDEAS

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    1. Yonghui Liu & Yongge Tian, 2011. "Max-Min Problems on the Ranks and Inertias of the Matrix Expressions A−BXC±(BXC)∗ with Applications," Journal of Optimization Theory and Applications, Springer, vol. 148(3), pages 593-622, March.
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