A new method based on the semi-tensor product of matrices for solving communicative quaternion matrix equation ∑i=1kAiXBi=C and its application

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A new method based on the semi-tensor product of matrices for solving communicative quaternion matrix equation <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:munderover><mml:mo movablelimits="false">∑</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo linebreak="badbreak" linebreakstyle="after">=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:munderover><mml:msub><mml:mrow><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mi>X</mml:mi><mml:msub><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo linebreak="goodbreak" linebreakstyle="after">=</mml:mo><mml:mi>C</mml:mi></mml:math> and its application