On solutions to the quaternion matrix equation AXB+CYD=E

By Qing-Wen Wang, Huasheng Zhang, Shao-Wen Yu. 2008

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Expressions, as well as necessary and sufficient conditions are given for the existence of the real and pure imaginary solutions to the consistent quaternion matrix equation AXB+CY D = E. Formulas are established for the extreme ranks of real matrices Xi,Yi,i =1 ,···, 4, in a solution pair X = X1 +X2i +X3j +X4k and Y = Y1 +Y2i +Y3j +Y4k to this equation. Moreover, necessary and sufficient conditions are derived for all solution pairs X and Y of this equation to be real or pure imaginary, respectively. Some known results can be regarded as special cases of the results in this paper.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/dcb26d36666a369ee855e1eab977577b3c14f3ed

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Citations in the corpus

• Split quaternion matrices (2012, background): “Because of this, various authors have been studied quaternion matrices, for example [1], [4], [5] and [6].”