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

Shao-Wen Yu

International Journal of Mathematics and Mathematical Sciences, 2012, vol. 2012, 1-19

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.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:307036

DOI: 10.1155/2012/307036

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