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The reflexive and anti-reflexive solutions of a linear matrix equation and systems of matrix equations. (English) Zbl 1198.15011
By using appropriate matrix decompositions, necessary and sufficient solvability conditions and explicit reflexive and anti-reflexive solutions for the following matrix equation: 9mm
(I)
$$A_1 XB_1 = D_1$$, and systems of matrix equations:
(II)
$$A_1 X = C_1, XB_2 = C_2$$, and
(III)
$$A_1 X = C_1, XB_2 = C_2, A_3 X = C_3, XB_4 = C_4$$ are derived and formulated, respectively.

##### MSC:
 15A24 Matrix equations and identities 15A06 Linear equations (linear algebraic aspects)
Full Text:
##### References:
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