The Real and Complex Hermitian Solutions to a System of Quaternion Matrix Equations with Applications
2012 ◽
Vol 2012
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pp. 1-19
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Keyword(s):
The Real
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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 equationsA1X=C1,XB1=C2, and A3XA3*=C3. Moreover, formulas of the maximal and minimal ranks of four real matricesX1,X2,X3, andX4in solutionX=X1+X2i+X3j+X4kto the system mentioned above are derived. As applications, we give necessary and sufficient conditions for the quaternion matrix equationsA1X=C1,XB1=C2,A3XA3*=C3, and A4XA4*=C4to have real and complex Hermitian solutions.
2019 ◽
Vol 35
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pp. 266-284
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2001 ◽
Vol 192
(4)
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pp. 565-576
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