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• W1998811839 abstract "The matrix equation<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M2><mml:mrow><mml:mi>A</mml:mi><mml:mi>X</mml:mi><mml:msup><mml:mi>B</mml:mi><mml:mi>H</mml:mi></mml:msup><mml:mo>=</mml:mo><mml:mi>E</mml:mi></mml:mrow></mml:math>with<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M3><mml:mi>S</mml:mi><mml:mi>X</mml:mi><mml:mo>=</mml:mo><mml:mi>X</mml:mi><mml:mi>R</mml:mi></mml:math>or<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M4><mml:mi>P</mml:mi><mml:mi>X</mml:mi><mml:mo>=</mml:mo><mml:mi>s</mml:mi><mml:mi>X</mml:mi><mml:mi>Q</mml:mi></mml:math>constraint is considered, where S, R are Hermitian idempotent, P, Q are Hermitian involutory, and<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M5><mml:mi>s</mml:mi><mml:mo>=</mml:mo><mml:mo>±</mml:mo><mml:mn>1</mml:mn></mml:math>. By the eigenvalue decompositions of S, R , the equation<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M6><mml:mrow><mml:mi>A</mml:mi><mml:mi>X</mml:mi><mml:msup><mml:mi>B</mml:mi><mml:mi>H</mml:mi></mml:msup><mml:mo>=</mml:mo><mml:mi>E</mml:mi></mml:mrow></mml:math>with<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M7><mml:mi>S</mml:mi><mml:mi>X</mml:mi><mml:mo>=</mml:mo><mml:mi>X</mml:mi><mml:mi>R</mml:mi></mml:math>constraint is equivalently transformed to an unconstrained problem whose coefficient matrices contain the corresponding eigenvectors, with which the constrained solutions are constructed. The involved eigenvectors are released by Moore-Penrose generalized inverses, and the eigenvector-free formulas of the general solutions are presented. By choosing suitable matrices S, R , we also present the eigenvector-free formulas of the general solutions to the matrix equation<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M8><mml:mrow><mml:mi>A</mml:mi><mml:mi>X</mml:mi><mml:msup><mml:mi>B</mml:mi><mml:mi>H</mml:mi></mml:msup><mml:mo>=</mml:mo><mml:mi>E</mml:mi></mml:mrow></mml:math>with<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M9><mml:mi>P</mml:mi><mml:mi>X</mml:mi><mml:mo>=</mml:mo><mml:mi>s</mml:mi><mml:mi>X</mml:mi><mml:mi>Q</mml:mi></mml:math>constraint." @default.
• W1998811839 created "2016-06-24" @default.
• W1998811839 creator A5081191482 @default.
• W1998811839 date "2013-01-01" @default.
• W1998811839 modified "2023-10-15" @default.
• W1998811839 title "Eigenvector-Free Solutions to the Matrix EquationAXBH=Ewith Two Special Constraints" @default.
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• W1998811839 doi "https://doi.org/10.1155/2013/869705" @default.
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